My BMS (Ji Kong JK BMS) is a common port, but it has separate control for charge and discharge protection. When it goes into under volt protect mode, it will not pass current out from the battery to the load, but if there is charge current coming in, it will still allow the current into the batteries to raise the voltage. And on the flip side, if the voltage goes too high and hits over volt protect, it will go open and not accept any more charge current, but if will still supply current out to the load. I have not tested the over current protection, but I would assume it works the same way. Testing the over and under volt was easy, I just adjusted the trigger voltages to make it switch off and on in each case. I was concerned it would be a problem switching off to stop an under volt, and then not being able to charge, but they thought of that and it works great.
I am setting my inverter/charger voltage limits to always stay inside of the BMS limits, so it never should go into protect, but the BMS will always be there as an extra safety factor.