Jamie Siminoff had flown to frigid Kiev, Ukraine, to give a pep talk to the roughly 30 people who worked there for his fast-growing video doorbell startup, Ring. It was December 2016, and the Santa Monica, Calif., company had recently opened a satellite office in Ukraine to develop products that would use artificial intelligence and motion detection to improve home security.

At one point during the meeting, Mr. Siminoff asked the team how he could make their jobs easier. One of the engineers in the room said that to improve Ring’s software, the Kiev office needed access to customer video feeds. The information trove contained images from security cameras pointed at home entrances across the globe that could be traced back to individual customers.