For Tamiya flat paints, I concur with Gerald. They can be touch dry in minutes, if not seconds when airbrushing but require at least 24 hours to fully cure. When fully cured they are quite tough.
Tamiya Gloss paints can be a different proposition. Because of the "hard" surface film which forms on gloss paints, the solvents can be trapped and can take considerably longer to outgas. Typically, Tamiya gloss paints can be prone to "fingerprinting" for up to 48 hours, and can take a week or more to fully cure. This can vary depending on thickness of application, tenp, humidity etc.