I think I’m over complicating it from poor memory, what the other replies above said about needing a ‘pure sine wave’ ups sounds right and should cover it. I think this is the same as being an ‘active’ or line-conditioning UPS.
The quick explanation is that AC power comes in as a waveform that oscillates up and down. When the mains power goes out and your generator comes up, the waveform it puts out wont match in timing to the mains one. Your PC PSU can’t handle that waveform changing suddenly. A suitable UPS maintains the waveform going into your PC even if the input power waveform changes, and can re-align the waveform slowly to match a differing input. Lower end UPS units don’t do this.