If it is a DC system, the charger has to have enough power to both charge the battery and run the load. If the pump can work with power on, and AC is on, and the battery voltage is rising, you have a well working system, and I would not bother testing any further.
For reference, the voltage rose becase you probably have a 3 stage charger, which means it will float @ 13.5, but will run an overcharge stage to 14.4 or there abouts. When the pump is on, the charger may have triggered to leave float and go into overcharge. If the battery is healthy, it will not be in overcharge for more than an 1hr. If you have a 2 stage charger (no overcharge), then you are just seeing some additional voltage drop becasue of the heavy current draw on the load.
For reference I design battery chargers for a living.