When I had my in-wall tank in Knoxville, I started seeing mold on the ceiling in the laundry room behind the tank. The large sump was in that room, and there was very little air-flow in there (it was an older home.) I killed the mold, then painted over it. I then installed a small bathroom fan and wired it to run all the time. It ran this way for a year or so, and then I moved out. I never had anymore mold issues.
From what I understand, moist stagnant air creates conditions ideal for mold. If you get the air moving, it helps alot with mold, even if its humid air.
Just my personal experience...
Jason