You don’t need to pay for the Premium upgrade again when you move to a new phone, the license is for life (as promised in the app description). What may cause confusion is that there are two alternative ways to upgrade to premium:
1) using the in-app-purchase button in the app (this license is restored automatically upon re-install)
2) using the stand-alone Premium Key app (which has to be installed on the new phone also, this time it will not cost any money)
I had to create method #2 because some users were either not comfortable with the IAP, or it didn’t work on their rooted and patched devices.
If the IAP checking is failing on your device for any reason, I can give you a full refund on the IAP and ask you to use the alternative upgrade method. For the refund I will need your order number (GPA xxxx-xxxxx-xxxx from the email Google sent you after the purchase, search for “Dyna logix” in your mailbox).