There are a lot of different concepts in your deceptively simple appearing question.
Mushrooms are poorly understood by most cooks, and there's a lot of misinformation. First, you absolutely can wash mushrooms. Fresh mushrooms are mostly water anyway, if they weren't, they'd be dried mushrooms. Dried mushrooms aren't anything like fresh. QED. That having been said, mushrooms shouldn't be soaked -- only briefly rinsed, and wiped off completely. You want them dry before you saute.
Second, most cooks forget what they're trying to do by sauteing. The goal is not to throw the food in the air. The goal is to brown it and cook it through as quickly as possible in a very little fat. In the case of mushrooms, that means cooking in a very little fat, and not overcrowding the pan. Just like searing, the mushrooms must have an opportunity to brown, and release before flipping them. Once they're browned -- with as little movement as possible -- you can start showing off your hot pan technique.
1st Rule for Saute or Sear: Brown before moving. Moving food too soon is one of the most common sins -- especially with men.
After they're browned the mushrooms can withstand a fair bit of abuse, so now's the time to start building the rest of the dish with whatever -- except the salt or very salty additions like soy sauce. Even at this stage, salt can make them tough and rubbery; to the extent that you can, delay adding anything very salty.
Finally, to answer your question, after the mushrooms are cooked but still in the pan, undersalt them. Taste and adjust. Plate.