I have Spectrum as well and my service stays on when the power goes out for at least as long as my UPS lasts. I don't have a generator (apartment) so I don't know for sure how long it lasts.
Not here in my experience. My gear is is all on UPS. It will all be up, but the second the power goes out, so does Spectrum.
Damn that sucks. I wonder if it has something to do with me being in an urban area or something. Maybe they have business customers with SLAs so they need backup power.