City water is already under pressure, so you don't need the pump. When the FW tank is being utilized, the water just sets there. It's not under pressure, so you need to use the pump to "suck" the water through the system. I guess on most models, there's no way to fill the FW tank(s) using the pump. You have to fill them using the gravity feed inlet, then turn the pump on to pressurize the system. Opening a faucet or two was a good idea, though, to allow air to escape the water lines. Also not a bad idea to "burp" the water heater by opening the pressure release valve for a few moments.
2013 Eagle 266RKS
2011 Ford F-150 w/3.5L Ecoboost & H.D. Tow Package