Is this generator supplying loads other than the pump? Single phase loads?

Even if the pump is the only load, good luck ensuring that the downstream
ganged breaker will trip first. If there are other loads (between the two
breakers), a gen breaker will almost certainly trip first.

What happens next will depend on what lies downstream of the (tripped) gen
breaker. Single phase loads on the tripped phase will end up in series with
the pump winding. While the voltage will probably collapse so that these
loads become inoperative, that leg will still be energized at some voltage.
If there's a fault there (what tripped the breaker), that could lead to a
hazardous situation.

Best bet is to replace the two gen breakers with a ganged unit. Don't feed a
line to line load from independent single pole breakers.

--
Paul Hovnanian
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Shoot low, sheriff. They're riding Shetlands!