You should give us some additional information about your Ethereum transactions:
(1) Deposit address
(2) The deposit/ receiving address does belong to exchanges or not.
If your answer is exchange address (of your account on exchange), the situation become clearer and easy to understand. Nowadays, most of crypto exchanges use cold wallets, it means after you send coins to your address on exchanges, they will be automatically sent to different address, that managed by the exchange, and in their cold wallets. Cold wallets are safer than hot wallets. So, you should not worry about that if it is your case.
And if after you log in your account on that exchange, your balance and history transaction show that the amount of Ethereum come to your account, it's fine, eventually.