Since the city water inlet and the pump outlet are essentially a common connection, the shower temperature shouldn't fluctuate with pressure variation, in theory.
That said, you may have a common type of pump that turns on at a low pressure point and off at a high pressure point as determined by the pressure switch. There is a normal air pocket trapped in the top of the hot water tank that by its existence acts as a cushion and while I can't grasp at the moment why this might contribute to your symptom I would try this. Allow the water heater to cool down, turn off the pump, open the temperature pressure relief valve (pop off valve), remove the drain plug to drain about a gallon or more of water. Replace the plug, allow the temperature pressure valve to snap shut, turn on the pump to allow the water heater to fill to re-establish the air pocket, turn on the water heater and test once hot.
That's my best guess.
Air Safe Hitch, Reese Dual Cam 800#, Centramatics