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

No bubbling or anything though.

Any oil based stain is going to leave some free residue and you may be
also surprised how long it takes to dry completley.

Oil based stains are pigment floating in oil. The oil acts as a binder
such that as it dries it holds the pigment in place. Oils can be slow
to dry, even though they all have driers to help things along.
Varathane is a soy oil based stain. This is I suppose a fairly new
concept and maybe not as well tested as the hundreds of years of more
traditional. How long does soy oil take to dry? How well does it bind
and hold the pigment. Before fully cured I would imagine any oil will
would free up some of the pigment.

If you are really worried about it, I would wait until you think the
stain is dry, then give it a good wipe down with mineral spirits or
whatever solvent varathane reccomends for clean up. I am sure you will
see some color come free.

I wouldn't worry about it. The Tung, if you didn't add driers or at
least mineral spirits will take a week or more to fully dry dry aloso.
Maybe more.