Katadyn recommends flushing the system with a bleach-water mixture after trips if you are not planning on using it again soon.
I don't know whether or not soaking the system in bleach overnight is any better or worse for the product. For what its worth my Katadyn filters have always gotten "black stuff" over time and I am pretty sure it is pond scum and the like trapped in there and not necessarily mold or mildew.