I put my purple out in the sunlight, on the concrete drieveway. I let it sit a couple hours then flip it to the other side. In half a day it's as purple as it'll ever naturally get. Another thing I have done for a long time is use an industrial hair dryer (heat shrink gun) on the cue as it's spinning slowly. It gives a deep & bold purple, almost unnatural looking. Once finished I have never had purple change color on me.
During the heating with a heat shrink gun, I have noticed the sap drawing up to the surface of the wood & it is a deep purple, nearly black. Logic tells me that this is the purple pigment that colors the wood. So why it becomes purple is pretty evident. The mystery is why it becomes purple. I know heat activates it, oxygen is reported to activate it, & light is reported to activate it. I have tried heat & it works. Natural sunlight works very nicely. FLR lamps work ok but slow. Letting the wood sit until purple works but is slowest. I even tried a UV light in a finish booth & it didn't do a dang thing. So it's a mystery to me. It turns purple. I very, very rarely have seen purple turn brown except for in very old, oil or shellac finished cues.