ps. The generator breakers tripped, wouldn't effect the PI unit would it???
I'm assuming that whoever installed your PI, installed it as most do which is on the output of the shorepower cord, which PI is then the input to the transfer switch. If that is true, then no, the generator breaker trip doesn't effect the PI unit.
Most transfer switches are set up, so that the generator has priority. 'IF' the generator is running and supplying power (ie, the generator breaker isn't tripped), then the transfer switch selects that input and passes it thru to the transfer switch output. That is irregardless of whether there is shorepower available or not.
If the generator is not running, but there is shorepower available, then the shorepower is passed thru to the transfer switch output.