ways fresh water tank get filled:
1) Via FILL valve at water panel.....valve not closed/leaking thru (if you have one)Exercise valve back/forth or replace bad valve
2) Via pump internal check valve...just a diaphragm that can get hung open with debris/stuff from tank.
Run pump using the water from fresh water tank....flush out pump by using it.
Then after using tank.....swap to city water and check if still back-flowing thru pump (disconnect suction line at pump and see of water flows out of pump)
If still leaking......install an 1/2" in-line check valve in suction line (Shurflo has them....$10 or so----pump still good)