I don't know where check valves would normally be in a system like
this, but what's happening is that when this valve is left on, it
creates a path between the hot side and the cold side without allowing
the water to exit when the sprayer is not in use. Also, the
recirculating pump must be supplying greater pressure to the hot side
than the cold. You could install check valves at that sink...or remove
the sprayer so people don't leave it on...