I would go as far to say that, the air pump is there to force water flow in this inverted tank with the water below, and as long there is flow under, the water will have enough oxygen.
It is the same thing as the small water lift pump that us fish people use on hang on the back , "weir", overflows to create and keep the initial siphon. It is just on a larger scale. The water is lifted because of the negative air pressure, not water pressure. so the fish are not experiencing any pressure difference. Or maybe the fish ARE swimming upside down!