Welcome to one of the frequent Montana problem. There is an anti-siphon device, for the black tank flush system, under the sink cabinet. Open the cabinet doors and look for two white plastic lines. Those are the lines to the anti-siphon POS. The red and blue lines are cold and hot water lines to the faucet.
There are lots of solutions to your problem. Replace the valve with a better one or eliminate the valve altogether. Do a "Search" on "black tank backflow" or such and you should find a lot of information. Here are some samples:
https://www.montanaowners.com/forums...+tank+backflow
https://www.montanaowners.com/forums...+tank+backflow
I choose to cut the line, eliminate the valve and splice the line back together with Shark Bite fittings. You can easily find the water lines for the flusher behind the pass thru wall. I use an anti-siphon valve on the black tank flush hose connection in the convenience center.