You don't get access to all the private keys of the Bitcoin addresses on a centralized exchange. These exchanges alone have access to your private keys. The possibility of your address been previously used is there but I don't think it's happening.

If your Bitcoin address is already in use, then you'll have access to its past transactions on the blockchain. Just check to confirm. Don't forget that the blockchain is A PUBLIC LEDGER THAT CONTAINS THE DETAILS OF ALL PAST AND PRESENT TRANSACTIONS.