No problem, the two answers here:

1/ You don't have duplicates because a Feistel network assures you there is no duplicates: every input has a different output with a fixed key in every round.

2/ If the secret is compromised anyone can issue valid numbers in the same way that if your secret encryption keys for encrypting your data exposes it. The idea is that the secret key material is never compromised as it is assumed in all security cases. You should custody with the right measures based on the attack vectors you have. The custody of secrets is independent of this method.

Please let me know if you have more questions.