My port starting battery was receiving a charge from the inverter even though it was not hooked up to the inverter. Could this be coming back though a shared device? If that is in fact the case would that also mean the starting battery is discharging when the inverter is in use?
An automatic combiner relay (aka voltage sense relay) will only parallel the batteries whenever there is a charging voltage (i.e. 13.3 VDC). As soon as the voltage drop bellows 12.8 VDC the batteries are separated and the inverter loads would only be applied to your house battery.