reliance transfer switch

The furnace either doesn't like the waveform the generator is making or is too big of a load. The clocks are probably just sensitive to frequency changes. You haven't posted any details so I'm gonna suggest a bigger, better quality generator?

I never liked transfer switches...saw an Inter-Lock kit once and that was enough of transfer switches for me.
That is so weird that the alarm clock GAINS time! As for the furnace not running, may not be wired to the transfer switch.