Even if they do then how do they confirm that the fund is connected to mixer?
By looking at coin history/lineage for deposits, as well as tracking where coins go once they've been sent from the exchanges to users, i.e. do the coins ultimately go through a CoinJoin mechanism further down the line?
Binance in Singapore,
for instance froze a user's funds after they were connected with a Wasabi CoinJoin.
Companies like Chainalysis have perfected the art of tracking Bitcoin and Bitcoin users and employ a host of techniques of identifying (Wallets / Entities / Clusters) through all sorts of analysis, which includes co-spending of inputs, change address analysis, amount analysis and unique finger-print style analysis of wallets. This means they are able to identify Gambling website entities and who is who.
CoinJoin transactions, by their very nature, are very easy to identify, even including which type of CoinJoin service you even used.
When exchanges use and integrate these Chain Analysis services into their systems, user's simply get flagged and the exchange is then capable of becoming a bully asking for further KYC checks.
So far, this flagging and policing hasn't been massively prevalent on a wide-scale. But it's possible that it may increase in the future.