Well, I think that you just fixed your moisture problem with the removal of the tree. The moisture and algea living in there should die soon, Bleach is great for this problem.
Just keep the area ventilated and will ample sun. Cedar is like a sponge when wet and this has to dry out properly. Keep things on the deck moving around after a rain for drying out. If things are on the deck, then build something where they are elevated or above the deck.
Consider a good sealer or penetrating oil like from the Flood Company, CWF_UV. This is super.