The instance where it was totally wet (the dust cap) was after a specialty dive with a different boat than our regular crew. Since we were taking our gear and putting it back on our regular boat, he grabbed the tank off my back and slapped the wet dust cap on. The other few instances were at the end of the day (our regular crew was more conscientious–they'd blast the cap with air before replacing it). It's possible I'm being entirely too paranoid about all this, but I'm a relatively novice diver (I now have ~40 dives) and my gear is new, so I'm feeling protective & still getting the hang of what is "officially recommended" vs what is standard practice.I have no idea why the dive staff would be putting the dust cap on when switching tanks unless there is a significant time delay in between. I would expect them to put the cap on if the dive day was done and breaking down gear. A short blast of air is SOP with the blast in the appropriate direction. But then again I am in the camp of thanks I got it because I pack my gear so to easily transport back to my room.
As for rinsing, during the dive trip I rarely rinse gear unless there is a easy to use dunk tank. And might just skip it depending on the water quality. At the end of the trip every gets cursory fresh water dunk with the BCD flushed out. Once at home everything gets a long (1-2 hour) soak and rinse. Regs are dried with the dust cap off. They are stored with the dust caps off.
As for rinsing AA regs. I tend to soak the second stage in and first stage out and above the second stage. Then swap.