Usually the pump output and city water join in the closed cabinet next to the bathroom sink. There should be a back-flow preventer at that junction or somewhere between that and the pump. I looked at our plumbing and it appears there is a possible back-flow preventer in that cabinet where the city water hose goes into the blue pex cold water piping. I also see something that looks like it could be a back-flow preventer under the bathroom sink, but we're on the road and I haven't been able to figure out a diagram to show what goes where. If the back-flow preventer broke, city water pressure would reflect back to the water pump, and if the pump loses its ability to act as a back-flow preventer when not running city water will pass backwards through it into the fresh water tank and overfill it.
Image ...211 shows the city water coming in on the left and looping back to a metal screw fitting (image ...542) which I think now is just a male to male adapter. I believe the blue pex it attaches to then runs into the bathroom sink cabinet and runs up to that black unit just under the counter (image ...803), which then runs through the white tubing to the pump in the next cabinet under the pantry shelves.
By the way, I am in those closed cabinets often enough that I put 4 Velcro patches along the inside edge of the covers, so I don't have to fuss with the screws each time. It will be real handy should you have a leak, but also for winterizing and adjusting the outside shower hose that is obstructed by the large black pipe in the first picture. It is the black tank vent and should have been routed differently. I have that on my 'someday' list.
As you can tell I am not a plumber and hopefully someone with more knowledge will join in the conversation.
Let us know your status with the problem.