Drying time depends on temperature and relative humidity. High humidity slows drying, high temperature speeds it.
Dry to touch: paint does not come off on finger or other touching object.
Tack-free: the surface is no longer tacky, or slightly sticky, but the paint can be deformed (say by a fingerprint).
Soft cure: paint no longer deformable, but not fully cured.
Final or hard cure: polymerization essentially complete.
Curing time depends primarily on temperature. Cool temperatures generally slow curing, warmer temperatures speed it up.
I have had no problem with Tamiya bonding to unprimed plastic, provided the plastic was CLEAN, and the paint was THOROUGHLY cured. That means not less than 24 hours at 68° F, preferably 36 to 48 hours. In fact, I generally use a light gray Tamiya as my primer!
Curing can be accelerated using a food dehydrator, which provides gentle heat and air flow. Be sure to wait until the paint is tack-free before putting it in the dehydrator, or you'll have a paint surface full of dust.