Don't think about coins sent as actual coins being sent. Think about it as an accounting entry into the public ledger that is not limited to a specific location, company or person. Any entry into the true and correct ledger (correct block chain) is there for any compatible application (exchange wallet in this case) to interpret and display. If you sent coins, the entry into the ledger has been made. As soon as whichever party in question upgrades their blockchain interpreter (wallet) so that it can read the block chain and know how many coins are assigned to each address at the current block height, the coins will be displayed at the destination address in their wallet.