Hi Sam. Whether or not the ink goes black should not really matter. The Hoya Conbipo Medlite C6 is an extremely proficient laser when it comes to the removal of permanent makeup. It usually only takes 2-4 treatments. Even if the ink did turn darker, it would still be removable with the Medlite C6. We've done it before.
You should rest assured and return for your first treatment. Good luck.