As better-than-expected earnings results drove the Dow Jones Industrial Average more than 500 points higher on Tuesday, paring last week's losses, CNBC's Jim Cramer became cautiously optimistic about the fate of the rally.

"When the Fed bears are away, the stock bulls will play," the "Mad Money" host said. "As long as the Fed doesn't mandate a slowdown, you get what we had today and what I bet we could have tomorrow."

While several technical indicators had signaled to Cramer that the sell-off could be short-lived, some key fundamental factors paved the way for the Dow to see its best trading day since March, he said.

Among them was an "absence of negatives" emerging from the White House, namely the lack of President Donald Trump's hawkish rhetoric around tariffs on Chinese goods, Cramer said.

The president did escalate his attack on the Federal Reserve, however, calling it his "biggest threat" because of how quickly the central bank is raising interest rates.

Also conveniently absent on Tuesday were more comments from the Fed on hiking rates, which some, including Cramer, believe can cause an economic slowdown in 2019.

"I'm not saying that the Fed has learned its lesson, but at least today investors felt safe ignoring our misguided central bankers," he said.

Then, five positive earnings reports from flagship Dow stocks compounded the positivity: UnitedHealth Group, Johnson & Johnson, Walmart, Morgan Stanley and Goldman Sachs all reported notably strong quarterly results.

All of these factors combined sent "the bearish arguments ... into hibernation" in Tuesday's trading session, Cramer said. But whether that means the bulls have effectively regained control remains to be seen, he warned.

Still, the rally gave investors who can't handle some continued volatility a way out, the "Mad Money" host said.

"If you want out, bye. Go ahead. Take it," he said. "If you hate this market, if you want out, you're getting a much better chance to sell than you would've gotten when things were falling apart last week."