There's a check valve between the tank and the water pump. When you're on park water, the park water pressure back-seats the check valve, preventing water from entering your potable water tank. (Sometimes this check valve is incorporated into the water pumps suction line, rather than being a separate valve in the suction hose.) It's probably leaking backwards. Try turning off the city water, turn on the water pump, and pump some water from the tank through the faucets. This should clear anything out of the check valve and let it re-seat. If that doesn't work, then your check valve is probably broken; you'd need to replace it.
In the meantime, if flushing the check valve didn't work: If your unit has a connection that allows you to pump antifreeze from a jug, then you may also have a valve between the tank and the pump that you could close to stop the back flow. Usually there is a Tee in the suction line, with a valve between the tank and the Tee and another valve between the antifreeze suction connection and the Tee. In this case, close the valve between the tank and the Tee.
I understand that some units have a 3-way valve instead of two valves and a Tee. In this case, the valve lines up the pump suction to either the tank or the antifreeze connection. If you move the valve position from the tank to the anti-freeze connection, the water will probably leak out of the antifreeze connection instead of the tank. It's possible that putting the valve in the mid-way position will stop all flow, OR it will route flow to both the tank and the antifreeze connection, depending on how the valve is constructed. I don't have one of these, so I can't tell you for sure what which way it will operate.
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