Tung oil, like all drying oils, will cure fully or through-harden as it's called in the paint world. This process proceeds naturally as oxygen reacts with the oil and it can't be halted, so no oil remains permanently wet under the surface in normal circumstances although it can seem that way in paint films because it can take a looong time. But this is very different, when applied directly to wood oils don't penetrate very deeply at all so the coat of oil is very much thinner and cures much faster.
But this is a slow-drying oil so don't read faster as fast, here instead of months to years it's weeks (at minimum).
dcmguy, depending on how scrupulously you dried the surface I'd be inclined to wait at least a couple of weeks, but waiting a full month would be safer. Drying and curing times are always dependent on temperature and humidity, because it's getting cooler unfortunately we're heading into much longer wait times for oils and oil-based finishes. Unless you can place the piece somewhere where it'll stay warm and there's good airflow which will greatly speed curing time.
