I'm not sure how they're actually intended to function, but since these bags go inside of the inflated raft, they wouldn't need to be fully inflated unless you were counting on them to act as some sort of redundant floatation measure (boats are required in some areas to have 3 chambers). I presume - perhaps incorrectly - that 95% of the time you would just add your stuff and close the drybags without topping up the air.
In situations where you do top up the drybags by mouth, I imagine most of the bag would be inflated just by virtue of filling it with stuff, so you're probably only dealing with a breath or two of moist air (pure speculation). That's not much and I suspect only on long damp trips would it be a potential problem. In this situation, you could store your sleeping bag inside of another dry bag inside the alpacka drybag. For example, store your sleeping bag in a 1oz silnylon roll top dry bag, toss that in the Alpacka dry bag along with the rest of your gear and then top up the air as needed.