First let me caution you that painted pressure treated wood will split and the paint will peel eventually. That is one of the side effects of the process used to stop the rotting process.

As for how long? Simple test. Hit the wood with a smooth face hammer and if no moisture comes to the surface it is ready for paint. In lumber yards, most pressure treated is stored outside where it stays wet and, again, due to the treating process requires a much longer drying time than non-treated lumber. In other words, it's not the treatment that determines painting time, but the wetness of the wood.