I've had the same thing happen. And it isn't white like silver/gray/white hairs, but rather PURE white just like you said. Personally I think it is damaged hair and as it heals it gets color back and then gets zapped later. I've had 6 treatments so far, but I do believe that it is gradually dying off. I prepaid for my eyebrows, underarms, forearms, and chest while they had a winter special running (extra 15% off packages and running a 25% off gift certificates that could be used immediately), and I'm planning on just having her do an extra pass of my facial hair area each session of that (they only charge $50 for a touch up).
My white area is MUCH sparser than before and I think when I finally am done with laser everywhere I will be able to wax it because it isn't so thick. But overall I still shave every day or two just to clear that stubble because it does kind of poke through and looks funny.