Can't find the thread now in which this was being discussed, but just
got around to putting some tung oil (that's 100 percent raw tung oil,
not one of the "tung oil finishes" with no tung oil in them) on the
piece I stained with Varathan, and I was surprised that some of the
stain came off on the rag.

So we have a further complication--tung oil to some extent dissolves
Varathane stains.

No bubbling or anything though.