There's no "it took a while" process. If there was, you may as well just say that Braig turned into a Heartless as a result of MX's keyblade, which should technically be impossible. Heartless are born as a result of hearts being taken over by darkness, to which that has nothing to do with heart extraction. Whatever the case was, if and however Braig became a Heartless, it couldn't have been around the time of his heart extraction.