Fish skin is a good moisture barrier. The moisture has to leave through the wood, mostly... and it's hickory. Give it plenty of time to do that. Put the bow someplace dry and wait at least few weeks. Then go back to the tillering tree and basically start over. You should progress quickly, just don't get ahead of yourself, and don't assume nothing changed. Assume it may have. Look for issues... especially stronger limbs under the skins. Sturgeon skin is tough stuff, at least as tough as rawhide. It may need nothing, but I sure wouldn't stain it and seal until I was 100% satisfied with the tiller after all construction, tillering, and 200 shots or so... like any bow.