Turn the pump off and it won't run.
If your fresh water tank mysteriously fills itself while connected to city water, then the check valve built into the pump is leaking, either from a bit of grit or something, or from age and wear. In the latter case, using the pump for awhile can sometimes clear it out; in the latter case, of course, replacing the pump or installing a separate external check valve on the pump suction line is the only real solution.
I would tend to suspect it's running periodically on city water because the tank is empty and it's pumping air and the check valve, etc. isn't airtight even if it is watertight. In that case, you might be able to get rid of the problem by having a bit of water in the tank and running the pump a bit to get the air out of the lines.
If you had any significant leak, you would presumably know it by now after being on city water for an extended period of time.