Pure tung oil is the same no matter what company packages it. There are lots of faux non-tung oil products sold like Minwax Tung Oil Finish that do not contain any real tung oil. Real tung oil is one of the least protective and least water resistant of any finish according to the Wood Handbook published by the US Forest Service and according to Jeff Jewitt and Bob Flexner two "experts" even the experts agree upon. Linseed oil and paste wax are the only two finishes less protective. I would certainly not recommend it for a long term outdoor use unless you are resigned to reapplication every few months.
Another fact of life is that there is no finish that stands up more than 1-3 years if exposed to continual outdoor condition. Moisture, UV from sunlight and changes in temperature will cause the finish to deteriorate, become cloudy, then crack and peel.
So, the choices are, an oil finish like Pure tung oil, a marine "teak" oil (just linseed oil with small amount of varnish mixed in, or a true marine non-poly varnish. The reason to avoid poly is that the UV in sunlight will quickly attack the polyurethane causing to quickly fail. Go to a real marine store and look for brands like Pettit, Wolsey, Interlux and, best of all, Epifanes. These are expensive finishes but last the longest.
What is the item you are trying to protect? The best protection for something that can be moved is to move it under cover whenever it's not in use. Or, spend the money to have custom covers covers made from an exterior material like Sunbrella.