The water system needs pressure to operate, so either shore (city) water or the pump must be present and active. But if cold water flows, the water system has pressure and you need not worry on that score.
If the relief valve is draining hot water or steam without any human intervention, odds are the tank is overheating. Could be a bad thermostat, even on a new rig. However, if you are saying you open the relief valve manually and get hot water, that only means the tank is heating as it should.
If the heater bypass in your Surveyer has a single valve that you turn to bypass or ot, then there is a check valve where the line exits the tank. That is probably stuck closed and needs to be replaced. If it has two valves, it may have a check valve as well. Are you saying there are two valves at the heater? A picture would help us figure it out.