As the warning above states, never send ETH or ERC20 tokens directly to the escrow contract. They will be lost forever. All deposits into an escrow must happen via the Deposit function. This can be done easily via the escrow app.
Clients should never use centralized exchange accounts to make deposits into an escrow. For one, they wouldn't be able to use the app to Deposit in the first place. Secondly, they wouldn't be able to Release funds to the raid party as milestones are completed.
Clients depositing from a smart contract account (such as a DAO or multisig) will need to ensure that the account can interact with other smart contracts (e.g. via Aragon Agent, Moloch Minion, or a Gnosis Safe contract interaction).