That makes sense. You said, they can detect from the lightning address if they are in the same mint? Is there a such thing as a mint provided lightning address? Do you know where I can research this further?
Discussion
Most of the popular ecash wallets, such as minibits, provide a lightning address, and you use their mint by default. I believe any sats sent to that lightning address from outside of their mint would be converted to ecash from their mint, even if you have added other mints in the wallet.
The same would apply to lightning addresses from other mints, like cashu.me or npub.cash. Ecash sent to the lightning address from a different mint would first be melted and sent via lightning, and then minted as ecash from the mint that provided the lightning address. Ecash from the same mint that provided the lightning address would simply be sent as ecash from within the mint, though.
FYI, I did some looking and I think the way Minibits does it is to just send a cashu token via DM and the wallet logic must parse the token and automatically redeem it.