How do cryptocurrency exchanges handle users' accounts? I recently became aware of the fact that exchanges have trading engines that execute all trades within the exchange itself, and not on the blockchains. That is to say, if User A sells to User B, there is no corresponding blockchain transaction transferring those coins. Instead, both users have accounts on the exchange which are debited and credited. A blockchain transfer only takes place during deposits and withdrawals.

Please explain the same case for currency like Bitcoin as it manages its assets using UTXO Model which is a record of unspent outputs. And for other currency like Ethereum using the account-balance model as the transactions aren't included in the blockchain. So, how they will reflect changes in the account of a user?
When you send funds to an exchange, you do not own the UTXOs created. They are owned by the exchange.

Exchanges use the UTXOs from all their wallets to process withdrawals. This means that if you were to deposit and withdraw coins with no trades in between, your withdrawal will still not come from the UTXO created by your deposit. It could come from any of the thousands of UTXOs owned by the exchange (comprising of other peoples' deposits).

It's similar to how your bank account functions. When you deposit cash, the cash you hand over becomes the property of the bank. From that point, any balance that you have solely exists on the banks' internal databases. If that database was tampered with or destroyed, no one can prove you had money there. If you were to withdraw cash, the notes you get back will not be the same ones you deposited, and were likely deposited by some other customer.

Similarly, when you send coins to an exchange, your balance exists solely in the exchange's  internal database system. As you make trades, this internal balance is debited and credited. When you withdraw, the coins come from a UTXO set that includes everyone's deposits.

This is also why it is recommended to only keep coins you are actively trading on an exchange, since it leaves you open to the possibility of an exchange losing your money.