Fresh water pump runs for 4 to 7 seconds

Yes it's normal to run a little after the faucet is off. You may also still have some air in the lines or water heater. It can sometimes take a while to get it purged out. Each time you run out of water and pick up air it will act this way and need to be purged again. As you use your rig also pay attention for the pump coming on when you have not opened a faucet. This can be an important indicator of a very small water leak. If you hear the water pump randomly kick on for just a second or so, it's because it has lost pressure. It could be internal pump/valve leakage but it's more likely to be a very slow leak around one of the fittings or hose ends.