Same thing happened to us today - there was a short at the GFCI outlet at the source and it melted the wiring insid. Scary cud have caught fire (its in the shed). You may want to look inside the outlets?
Wow - I sure hope that some Jandy expert comes along and explains some built-in feature for that, but I'm thinking that it's something else. Like a bad connection somewhere. You'll want to have your electrical feed for the pool checked carefully.
There are some devices which delay power-ups to protect systems like air conditioner compressors, but those delays are usually about minutes. 4-5 hours? Not so much.
Try and pay attention to the start and stop times. If my theory is correct, (clock reset to midnight when power went off, just like a good old VCR) then it will be going on and off at different times than it did before.
A bit late but this might provide some insight and more importantly some peace of mind.
A while back I was having a weird problem with a Pentair pump, unrelated to your problem but I think I stumbled onto your answer nevertheless.
In the course of diagnosing my problem I was directed by Pentair to the manufacturer of the motor of the said pump.
My question was related to input voltage.
The technician explained to me that all their pool (pump) motors have a built-in reset on them that would trip if the motor is not turning at the design rpm. (so my issue was not voltage)
My guess is that a power fluctuation before or after the outage would have altered your motor rpm therefore tripping this built-in reset.
According to what he told me, it resets by itself after a while but did not specify what "a while" was, neither did I ask.
Not sure if that is what happened to you but it certainly fits.
Hope this sheds some light on your weird event...