You've got multiple issues here that are confusing everybody.
The NFC Ring Control App doesn't require ring registration to work.
Ring registration allows you to verify with the NFC Ring Unlock App and use it.
This doesn't require a ring for registration if you just follow the listed instructions exactly and don't use the ring once.
You don't need the ring to register in the NFC Ring Unlock App, and the NFC Ring Control App doesn't require you to register before it will work.
These are totally seperate to the ring reading issues you're having which do seem like firmware issues from what Nairod has said.