I generally seal the back of the bow with a thin layer of TBIII let it cure overnight then add the skins with TBIII. This sealing helps to keep new moisture from entering the wood.
I skinned an osage bow a few years ago and after a few days realized it felt mushy and had lost 10# of draw weight. I set it in my utility room for a week and it came back to life and back to it's intended draw weight. After that I began sealing the wood before adding the skins. I still give a newly skinned bow at least few days to "cure" before stressing it.