Wouldn't that depend on your setup?
If your tubs have no holes and the thermostat probe is not in the tub the temp in the tubs would start to increase as the eggs get closer to hatching. I am sure the temp inside the incubator would start to increase as well due to the tub temp rising but not as much as inside the tub.
Now if the tubs have holes then yes I agree that the thermostat would regulate and not turn on since the hotter air is moving out of the tub into the incubator.
Not the expert just asking