If that's how the exchange transaction work. So, what the reason behind some exchange site charging their account holder some certain fee for making deposit since the network fee is not needed to be pay to miner?
It depends on the cryptocurrency.
To initialise a ripple wallet you need to have a minimum of 20 XRP
as a reserve so some exchanges like Poloniex charge you that 20XRP to create a wallet.
For ethereum there is a challenge on how to store user funds -- as an address or as a smart contract. They can either initialise a smart contract for every user (which consumes gas for contract creation), or create a new address (external Account) for each customer which will also incur gas fees for moving the deposited eth by the customer to the cold wallet. (It's worse for tokens since they'll have to seed every address with ETH for gas in order to move the tokens)
Some exchanges externalise this cost to customers by requiring a deposit fee so they can move the ether or tokens deposited, while others eat the cost.