Would NFTs on L2 cause token duplication since minting can technically occur on either chains?

I have recently thought about having NFTs which can be minted along the way. That is, when I produce a new artwork, I mint that artwork with a new ID on my token contract. So all tokens aren’t predetermined and are minted along the way.

I’m deploying my token contract on both Ethereum and Polygon so that I can mint on either one of the network and token owners can bridge tokens between the networks too.

However, something come to my mind when I deploy to Polygon. What happens if I accidentally minted the same token ID on both the networks? Wouldn’t there be an issue of duplication? How am I going to know which one is the real one or which one came first? How can the token owners trust that the minter wouldn’t mint a same token ID on the L2 chain?

For example, the minter could have minted token ID 999 to account 0xabc on Ethereum. A few days later, the minter accidentally (or maliciously) minted the token ID 999 again but this time to account 0xdef on Polygon. How are we going to tell which is the "real" token?

Do all NFTs having an L2 sidechain have this problem too since the minting can technically happen on either chains? How is this usually resolved especially for the kind of NFT I’m trying to build?