Understanding cryptocurrency exchange working
When users deposit cryptocurrency into an exchange, the exchange takes custody. The cryptocurrency is now the exchange's and the exchange adds a corresponding balance for the depositor to their books. The user specific address is only used to identify whom to credit the deposit to. After the deposit, there is no reason to keep track of the funds in the context of the user. 


  So, now his actual balance at his public key would be 8 BTC.


Tracking all trades on the blockchain would be incredibly inefficient. Rather, the exchange updates the user's balance in their books to increase the ETH amount and decrease the BTC amount. Any balance changes of the user on the exchange are only tracked in the exchange's books until the user withdraws from the exchange. When they withdraw the exchange sends an on-chain transaction to the user and reduces the user's balance by a corresponding amount.