One of the more frequent problem is that the check valve at the watyer pump is not sealing well. I tried to look at the parts drawings here:
https://catalog3d.winnebagoind.com/menu/Parts.htm
But when looking at the tubing behind the plate at the wet bay where the hose connects it becomes such a spiderweb of tubing that I was not able to trace out the exact flow in any way that I could snip a picture to show you how it can do this.
Maybe word description will work?
What we often find is that there is a path for water to flow to the tank when a valve is set correctly as you mention and then a different path when the valve is set to normal. On that second path there is a small plastic type "check valve" which is a pretty high class name for a simple flap that falls into place to stop flow from that direction!
What happens on older is that flap gets stiff as it degrades and it no longer fully stops the water going to the tank.
That requires replacing the flap portion of the pump. A small kit of parts and not technically hard to do but getting it out and back in can be a trick, depending on location.
On a newer RV, I might be more inclined to think the flap has some bit of debris stuck in the opening!!!
One way reported to clear this is to turn water on/off in sudden bursts to try to hit the debris with enough force to make it move!
I would first go for trying to make it clear by turning the faucet pressure on/off several times and also hitting the pump severla times hoping for a bit of luck?
Newer Rv tend to have small scraps of plastic at different points where holes and tubing have been installed and this junk can get into just the wrong spot at times.
For more info a search for "RV water pump check valve" can turn up lots of videos and articles on what you may find.
Hope for the best but be ready for the worst? Good luck to you!