Let me get this straight, this UPS is only hooked to one of the branch
circuits, not the mains.

If I'm correct, there are only flourescent lights as a load here. Is this
correct ?

If so I have an opinion that might help. Before these lights fire up, they
present almost no load. With no load the proximity to the other wires and other
factors may be impressing a "hum" on the output line. If the logic control in
the UPS detects this it may either see it as a fault, or who knows.

Flying by the seat of my pants here, I'd connect at least one incandescent
light to the output and see if it corrects the problem. I think it's worth a
try at least.

JURB