Since temperature and humidity are factors drying times of all finishes, let the piece dry until 1) it's not tacky to the touch, and 2) there is no smell at all from right up close to the surface - then wait a week. 😉
Be gentle with the buffing - all drying-oil finishes are 'semi-' hard as opposed to epoxy, water-base or acrylic finishes which become rock solid. Tung oil is one of the softer oil finishes and can easily 'melt' with high buffer speeds and firm pressure. Tung oil is added to varnish to form 'marine' varnishes - a flexible varnish that expands and contracts with the wood, versus a standard varnish which can crack (they even make a crackling varnish for antiques.)
If you are powering the buffing wheels on your lathe, a slower speed (under 800 rpm) and presenting (not forcing) the piece to the buff should work OK. For harder finished surfaces, using a speed of 1200 - 1500 rpm will work OK as well, provided you don't have lots of details, coves or vee cuts.
In Allan Batty's Hand Thread Chasing video, he uses slow speeds for areas that have high detail and can 'get right in there', while faster speeds for large areas with simple shapes. (He buff's the threaded box project.)