In part, yes. There's a lot more to the whole incident, though, that goes beyond even just the actual physics of what happened.

Chernobyl was built at a time when the USSR was moving in a maybe slightly more progressive way. There were definite factions in the government that did not agree about what the reactors should be used for. The new guard, as it were, wanted a set of power reactors. Regular old PWR/BWR things. The old guard wanted to produce power too, but they also wanted weapons material, because what is the USSR without more plutonium? In the end the old guard got what they wanted and the Chernobyl reactors were designed and built with the dual purpose of providing power AND breeding weapons material.

These two goals are very different from one another. Power reactors want to generate lots of heat for very long times so you can make steam and drive a turbine. Weapons breeding requires you to expose large amounts of U-238, which is a parasitic absorber in virtually all modern (not CANDU) reactors. And you can't just leave that 238 in the reactor after it absorbs a neutron to become U-239, for things to work well you have to pull it out pretty quickly. About one month of irradiation is probably where you want to be in general. So you have this dual goal of being able to run for long times with stable fluxes, but also wanting to be able to put lots of absorbing material in there that you change out entirely very frequently.

In order to meet both of these goals they reached a really weird design that was pretty similar to the CANDU system. They had these fuel rods, loaded with 238, that were cooled by a water channel around them, which they could pull and refuel while the reactor was running, in addition to the graphite moderator that didn't move. In order to be able to shuffle things in and out easily for the breeding portion of the mission they opted to forgo the heavy containment buildings and instead built what was basically a standard warehouse around things, nothing anywhere close to the things that we build around western reactors.

So now that we know a little bit about how the reactor is built and how that differs from normal construction we get to learn a little physics. This may have been covered earlier, but here we go anyway. When a nuclear reactor is "critical" it means that for every neutron that causes a fission event, on average, one neutron that is produced will go on to create another fission event. It's just 1:1 replacement on your fission neutrons. Fission almost always produces more than one neutron, but you lose them along the way to escaping into space or absorption in non-fuel things like the steel, control elements, or even just an absorption in the fuel that doesn't cause a fission. Because of physics that I'm not going to go into here, slower neutrons are better at causing fission. Think about putting in golf, slow putts are more likely to go in where the fast ones can skip across the hole or bounce out, etc. So in basically all reactors the goal is to make neutrons through fission, slow those neutrons down in some sort of moderator, hope you don't lose them along the way, and then get them back into the fuel to cause another fission. The slowing down process is done usually with materials that are light (carbon, water, heavy water, etc) and that don't absorb many neutrons.

So back to Chernobyl: Chernobyl has a setup that is common to many nuclear reactors. About 7-10% of the heat actually comes from the decay of fission products in any given reactor. This means that if you shut down you are still producing 10% of your maximum power level and need to remove that heat to keep things from going bad. Usually reactors get this power from the grid, but in the case of an emergency that might not be an option so they have onsite diesel backups (a contributing issue at Fukushima was the loss of these backups). At Chernobyl these diesels take more than a minute to start and reach full power, leaving the reactor without full cooling for at least a minute. Some clever scientists/engineers want to see if they can pull rotational energy off a turbine to help cover that minute of downtime while the backups start. They tried something similar a few times before and it was unsuccessful each time. So they devised a test where they would drop reactor power, but not below 700-800 MW or the turbine wouldn't have enough inertia to carry out the test, scram the reactor and test the system that would pull power from the turbine as it spun down. They don't bother to clear this test with the USSR's nuclear regulator, because why would they? Oh, and the guy that devised the test is an electrical engineer with zero nuclear experience.

They train the day crew on what is going to happen. Night crew begins to ramp power down as planned, but another power plant goes offline unexpectedly and the power dude from Kiev calls and says "Hey I need the power, can you not do the test?" and he's pretty important and living in Siberia is lame, so they postpone the test. A lot. During they day they go ahead with some of the preparations though, which include disabling the emergency core cooling system (ECCS). The day crew leaves and evening crew comes in. At 23:00 they finally get the call from Kiev saying they can go ahead with the test. Everyone who was trained on what was to happen is long gone. Night crew will be back in an hour, so starting the test now would mean a shift change in the middle of the test. The evening crew begins to ramp the power down further from the current 50% of maximum. Somewhere shortly before 1 am they reach the desired power level but there is an issue. One major fission product is a gas, xenon 135. Xe-135 has an absolutely gargantuan neutron absorption probability, this shit is the hungry hungry hippo of the reactor world. They have been producing it at a pretty stable level for a while, but now they aren't making as many neutrons as they had been and there is more Xe-135 than they can deal with and it's taking so many neutrons they can't stay critical. This is a phenomenon called xenon poisoning and it's one reason you can't immediately restart a reactor that you shut down, you have to wait for the xenon to decay away. So now power is on a steady decline that they can't do anything about, and power is going well below the 700 MW that was the minimum safe number. They end up at like 30 MW, less than 5% of the minimum safe power, and need to fix the problem. To try and fight the poisoning they withdraw a bunch of the control elements from the reactor and try to bring it back to critical, but to do so they have to disable the automatic controls for the rods and go to manual mode. Because the reactor is so complicated by the dual purpose design the operators don't like manually adjusting the control rods and the process is not something they are super comfortable with. To get back up to power they withdraw more control rods. They eventually get back up to 200 MW. During this process they are getting lots of alarms that they ignore.

So the reactor is in a bad way already. There are too many rods withdrawn, the ECCS is disabled, the operators are in manual control mode, there is a ton of xenon in the system, and the crew is totally untrained on the experiment. They turn on some extra pumps, as was part of the experimental plan. This means the water is flowing more quickly, which means less time to dump heat in the turbine, which means the water entering the core is now warmer than usual and therefore closer to boiling. As a result they are getting lower steam pressure than is safe and some more alarms trip. In response they shut down two pumps and reduce flow to build up steam pressure, but because water does absorb some neutrons the now cooler water has fewer bubbles in it and is absorbing more neutrons, lowering power. They withdraw more control rods to compensate. Of 211 control rods there are now 18 in the core. The minimum safe number is supposed to be 28. The automated system to insert all the rods in the event of an emergency was bypassed in order to maintain this state.

They begin the test and shut off the steam to the turbine. The diesel generators start up and begin to pick up the coolant pumps and in the mean time they are relying on the rotational inertia of the turbine to power the coolant pumps. As the turbine slows it produces less and less power and the coolant pumps are slowing down. The water in the core begins to heat up and starts to boil in the core, which is really bad. Steam has a much lower density than liquid water, and in a normal reactor this means you have far less dense moderator and your neutrons just don't slow down and your fissions stop happening. That's all well and good, but the Chernobyl reactors don't have water moderator, they have graphite which isn't changing density for shit. So the water wasn't a moderator it was actually a poison, absorbing a small number of neutrons, a function that it is no longer doing very well as steam. Reactor power spikes and more of the water becomes steam, and this process continues in a positive feedback loop, flashing all the water into steam and increasing reactor power. This is the positive void coefficient that Three-Phase mentioned. 12 of the control rods are still being handled by an automatic system and it is doing its best to keep things from going pear shaped, but way too many rods have been withdrawn manually and can't do very much.

So reactor power is on a sharp upward trajectory and for a reason than no one knows an operator hits the emergency shutdown button (SCRAM). The reactor begins to insert all the rods into the core, but this process will take 18 to 20 seconds for the rods to reach full insertion. For comparison the tiny research reactor at my university has to be able to drop rods in under a second, we test every year and it's about 200 ms for us to drop. So these rods are slowly making their way into the core, but they have graphite tips on them. Graphite being the moderator in the system. As this graphite displaces water in the core power jumps dramatically and fractures the fuel, trapping the control rods at 1/3 insertion in the core. With no control anymore and reactor power on the rise in a positive feedback loop, the reactor goes prompt supercritical, which is the worst thing a reactor can be. Prompt supercritical is the realm of bombs.

Reactor power was at one point all the way down to 30 MW. 100% power is 3,200 MW. In a matter of seconds after the control rods get stuck the reactor reaches an estimated 33,000 MW or 10 times full power. Things have gone pear shaped. The reactor explodes, but remember how they didn't build a containment structure so it would be easier to make weapons material? Yeah, there's no containment structure to impede the flaming radioactive graphite and various other reactor parts that go flying. You know most of the rest I'm sure.

It really was a chain of very bad decisions from the very start of the reactor design all the way to the events of the day of the test that lead to that disaster. If they had built a single purpose reactor this would never have happened. If they had built a containment structure it might have happened, but the disaster would be well contained. If they had consulted anyone from the regulatory agency this would never have happened. If the test wasn't postponed this might not have happened. If so many safety systems weren't bypassed, this would never have happened. Etc. There were so many things that they had to do to get this exact set of circumstances that it's never going to happen again. Probably the biggest reason is that no other reactors have been built like that, with those specific details that were made necessary by the dual purpose of the reactor.