wishuwerehere, I don't think that the city water will automatically fill your hot water tank unless you first open a hot water tap. (I am pretty sure that's true, but not positive, since I have never done it that way.). My reason for thinking that is that if there is no faucet open in the hot water system while you are in the process of filling it, then you will have back-pressure due to the air in the hot water tank.
So opening a faucet allows that air to escape, which then permits water to flow into the hot water tank. Once the faucet stops sputtering, all the air has been purged from the hot water tank, replaced by cold water (soon to be hot water, if your water heater ignites successfully).
I know for sure that the city water connection will not fill your cold fresh water tank -- it bypasses the tank.