So, when they cease those coins, how sure are we that they will take it to the government?
Exchanges would not just send the money to the government without concrete information that it came from a proscribed source. They should also maintain constant communication with the client on the latest developments relating to the deposit. They would also have to show proof that it has really been transferred to a recognized government wallet.
Sometimes, after making such deposit, before the exchange detects it, you must have traded the Bitcoin to Fiat and withdraw it to your account, so what will the exchange do after you have already withdrawn the money to your account before they later found out that the coins was tainted?
Exchanges don't have control over your personal wallet, so they will do nothing. But they might put your wallet under watch and wait if you would deposit in the exchange anytime in the future. They might cease any future deposits and ask for clarifications for your past transactions.
Another thing that just popped in my head now is, what if after you deposited the Bitcoin because you needed some money and wanted to convert the Bitcoin to Fiat, but you later changed your mind and you decided to withdraw back the money to a newly created address, will the casino report that your address to be flagged?
This question will depend on the terms of service of the exchange. It will clarify if you have erred by just depositing such funds or by using their services.