Another way to identify this generation is to look at the specific problems that plagued the machines before transistors, and check which technology actually fixed each one.
Vacuum tube computers suffered from four major issues: they were physically enormous because each tube needed its own housing, they consumed very high amounts of electrical power, they released so much heat that dedicated cooling was required, and they broke down often since the tubes would burn out much like an incandescent light bulb.
The transistor addressed every one of these problems directly. Being a small solid-state device, it allowed computers to shrink drastically in size. It needed far less power to switch on and off. It ran much cooler, cutting down on heat-related failures. And because it had no filament to burn out, it was dramatically more reliable over long use.
Since this exact set of improvements, smaller size, lower power draw, less heat, and greater reliability, is the historical marker that separates the transistor era from the vacuum tube era before it, it points to one specific generation of computing.
Therefore, the correct answer is Second Generation.