This is a wrong conclusion. You should not consider then as tumbling service nor use them as a substitute for a mixer. The coins do get pooled and the exchange will draw coins from the pool when someone asks for a withdrawal or add coins to the pool when another person deposits. But this does not change or affect the taint in the coins if already present. Some people have tried to use exchanges as modes of money laundering and got KYC-blocked on their accounts, which followed all these AML/KYC regulations on exchanges nowadays.

Still if your objective is to mix the coins then done use exchanges for this purpose.

For most if not all exchanges.

1. You get a personal deposit address
2. Anything sent to this address is then transferred to offline keys for the exchange.

When you want to wirhdraw:

They have an address loaded with a certain amount of coins, can be anywhere from a few btc to a few hundred. This is what you receive so its pooled inputs from everyone else who deposited previously. Exchanges don't expect you to pull out the same as what you put in also and the amount you get out will be below your wallet balance as they'll take up to 0.001 in fees (unleas it's coinbase who I'm told don't take a fee).