Formby's were1 rather infamous for their "Tung Oil Finish" because it isn't tung oil and actually never contained any. It's a cornerstone example of how product names in the wood-finish market are unregulated and can be very misleading!
"Tung Oil Finish" is instead a product very similar to (or identical to) what other manufacturers sell as "Danish oil" — a simple blend of oil and varnish, with added solvent to make it thinner.
And it's the solvent component that is likely the main culprit here as any product with some solvent in it2 can redissolve partly dried oil-based products that were applied previously. While you let the stain dry for 3 days even in warm and dry conditions this might not be long enough for complete 'drying' (i.e. curing). Curing takes considerably longer than the touch-dry time.
Also, if the door is indeed maple this is a dense, close-grained wood that doesn't absorb stains well. So it's likely to be contributing to the problem as some or a lot of the Old Masters stain may simply be sitting on the surface of the wood, readily wiped off. If you didn't thoroughly remove the excess as per the applications guidelines3 you could find that even wiping with a dry cloth could noticeably colour the rag or paper towel.
1 Now Minwax.
2 And there's more than 50% in "Tung Oil Finish"!
3 E.g. "Before the stain dries, wipe off excess stain with a soft cloth, first across the grain, then with the grain."