I don't think it is a problem. After an appropriate curing time remove the tubes, wipe off the excess glue and let the bow cure another 24 hours and you should be OK. I think the glue under the tube was like keeping it in an air tight container so it didn't cure out. The glue in the joint should have cured fine because the wood and boo absorbed the excess moisture.
Tite Bond has a good tech support. I have called them before and I got good friendly info. If possible, give that a try.