I can only guess, but my guess is once you have the tokens you need to register them yourself, otherwise you would lose them anyway. My guess is it associates the ETH public address with the EOS public address registered. Then when they take the snapshot, they look at the EOS-ETH tokens in that account. So when they are exchanged, they would have to be re-registered to be valid for the snapshot.
I am also going to guess that exchanges may permit people to register their tokens before the snapshot, however, this does cost money so it may not be free.