The UPS is too small.

A ballast typically operates at 5-10% over whats listed. The cheap ones operate at 5-10% under whats listed. My guess is your 425 watt UPS is probably truly overloaded. If you have a dimable ballast, try turning it down a notch or two, this should solve that. If its not a dimable then your kinda SOL on that.

Definitely put the fan on a different plug though. I would unplug the fan, and cycle the UPS and ballast to see if it makes a difference, if not, get a bigger UPS... Or to solve your power flickers, replace your breaker in the breaker box... Should be alot easier than buying a UPS.

- Edit addition:
Wanted to add, that just like ballasts, cheap UPS's can operate over or under specifications. You might only be getting 385 watts out of it. Another option... Open the UPS and remove the stupid little speaker.