There are only 2 ways for city water to get into the fresh water tank.
1. The built-in check valve in the water pump is leaking, allowing the city water to flow backwards through the pump into the tank.
2. The "city fill" valve is leaking when in the City position.
If, when using the tank/pump only, the system loses pressure and the pump cycles occasionally, that would point to the pump check valve. To verify, disconnect your line from the tank at the pump. Now turn on your city water. If water leaks back through the pump, then it's the pump's check valve. If not, you know that it's the Anderson valve.
IMO, any time engineers come up with a single unit to address multiple configurations, they are asking for trouble (and I AM an engineer). A 4-way valve (such as the Anderson) is an overly complex part for a fairly simple function. My Itasca has a simple 2 position valve for either city water or tank fill, and another (elsewhere) for winterizing. While either CAN fail, a 2-way valve is less likely than a 4-way valve to do so. Unfortunately, it would take some re-plumbing to convert your system in an effort to eliminate the troublesome Anderson "kantleak" valve.