First: You are winterizing wrong pumping all that noxious chemical into the lines, Blow 'em out with compressed air,, Like 10 times with a few minutes between blows.. Then if the air in the lines freezes.. Well if that happens the RV will be the least of your problems (Breathing being problem # only)
Now: Best guesses as to the answer to your qustion.
1: I have never heard of a quarter turn valve that is directional, but.. Possible it is
2: Defective valve.
3: I have heard of handles being installed wrong.
4: And valves not turned fully to stop.