Stupid Question About Water Pump

There is a tee in the plumbing that has city water connecting into the cold water piping. The same tee has cold water coming from the pump into the system. From there city water or water from the pump flow into the system. If everything works like it should the pump pressure usually is lower than the city water pressure. When the water pressure in the system reaches the pump set pressure the pump cuts off. If the pump is turned on at the same time you are connected to city water the pump will not run because the city water flows through the system and back through the tee increasing pressure against the pump pressure switch and check valve. The pump senses the pressure being higher than the set pressure and the pump will not run. If the pump is running and pumping water from the tank and you connect to city water the pump will shut off since the pressure will rise above the pump set pressure. The pump will only run when one, you are not connected to city water or two, the city water pressure drops below the pump set pressure while you are running water.