I got a couple of Aqua Lung DIN caps to replace the worthless rubber mini-caps that came with our Sherwood DIN fittings -- that didn't even reach the threading, and kept falling off.
The Aqua Lung cap has a blind hole in the bottom (top?) of it, into which the orifice fits. The fitting's o-ring then seals against the area outside of the hole. Seems to work, but you obviously have to be real sure the caps are screwed all the way down. Other caps are designed the same way; but it's hard to tell from Internet sites -- you'd have to buy one from a shop in person where you could examine it, or get someone's recommendation.
I don't think there's any real need to soak a first stage extensively. I'd imagine you'd have ambient air pressure inside the fist stage as soon as you remove it from the valve; even a few inches/cm of water would cause enough overpressure to start forcing water past the threads, if the cap isn't o-ring sealed. I don't think that would be a problem with a swish lasting a few seconds.
Alternately, an instructor once told me he just puts a finger/thumb over the end of his fitting while swishing it in the rinse water.
*edit for Pants*: Not all DIN caps are designed so that the o-ring seals inside the cap. A lot of inexpesive "delrin caps" aren't -- like the ones with hexagonal heads. Ask me how I know...
--Marek