We seldom hookup to city water but one time that I did, it did fill the tank and partially flood the site. For a quick and inexpensive fix I installed a check valve on the pressure side of the pump, not the suction side. It works great but it does reduce the pump's flow. This is really only noticeable when flushing the toilet and using the filtered water for cooking. We have one of those deck mounted upside down J faucets for filtered water in the kitchen.
Flojet does sell rebuild kits for some of their pumps, maybe all, but I have had other pressures(pun intended) to worry about.