DrewE - I think you have it. I've been staring at photos of the rig's plumbing compartment and (I've been) drawing diagrams. There is a single valve on the cold inlet to the tank and a check valve on the outlet. In normal mode any pressure in the hot tank will push on the cold system and any pressure lost in the tank when a tap has been opened needs to be replenished before the pump shuts off. In bypass mode, there is no air bubble in the tank to affect things.
I suppose if it really bothered me that it takes the pump a few seconds to shut off, I could add a check valve on the cold feed to the tank. It doesn't.