Had this happen to our Tiffin on the water tank filling just as you mentioned. Also happened to a bunch of other people, various makes and models. I can't remember if it was the check valve or what. One temporary fix (for that unit), was make sure I was at 40-50 psi on my regulator from the city connection. If more than that, it was going to be full. That's just a temporary fix and the check valve and / or pump needs to be replaced.
If it were me I'd just change the pump, and upgrade to a better variable speed shurflo. Those are nice, as they change speed depending on water demand. No cycling like the standard pump. Easy plug and play if you can get to it fairly easy. I agree with Dave. Maybe an accumulator tank, but that only band aids the problem as the pump shouldn't do that. I've have had them do that on a small bathroom faucet, but not on the shower.
John and Rebecca Dickson
Emma-7 / Little John-5 / Iva-1
Full Timing Again, Rev B
2013 Ford F-350 Lariat CC LB PSD
2015 SOB TT - With OC's Awning Poles (#8)
At least in Heaven, RVs will be perfect, and I won't have to keep fixing them.