HELP! Fresh water tank filling when valve set to “City”

Is it possible you're connected to the wrong inlet? The black star shaped thing at the lower left of the pic looks like it could be your city inlet. Undo the hose, connect to that, leave the valve on 'city' and see what happens. Be sure to use a pressure reducer.
The inlet that you're connected to may only be for filling the tank. Seems like it would be more clear if that valve simply said 'open'(city) and 'closed'(tank full).