The exchange i assume your talking about is changelly, changelly is a centralized exchange meaning they hold on to the funds while trading is taking place. This is usually done in hot wallets just like we normal users use , For much bigger transactions they could be using a hardware wallet for cold storage. But changelly is a bit different as you only send them crypto for each trade and you get whatever you want it converted into right in you other wallet, This minimizes the amount of time your funds are at risk.