Hi Jonathan, I have a similar problem but have not paid yet. I posted my query on the forums a while ago which you may want to read. I am sure your money is safe with Apple. I am guessing the following are the conditions for a successful developer program purchase:
The device used for downloading Apple Developer App should be linked with the Apple ID that you are buying the developer program for. (In my case the Apple ID linked with the device is different from the one which is going to own the developer program and therefore, (possibly) I am unable to enroll through the Developer App)
Make the payment with the credit card (I understand that the Apple Developer App allows more payment options)
I am assuming that in your case the Apple system read the difference in the Apple IDs later and finally made a rejection.
I have sent my query to Apple and expecting a response from them on Monday. My above guesses may well be wrong!