I will share my own experience. Binance freezes my funds when I receive funds from my clients. Because one of my clients sent BNB from a mixer. However, eventually Binance returned my funds but restricted my account, so I can't use Binance anymore.
I think binance has different ways of treating same issues, I've once received funds from a client which I suspected was sent through mixers or a flagged address, They notified me of their suspicion via email and app priority notification instructing me to provide more information about the transactions with a deadline to reply, else my account would be restricted.
I promptly replied with even images proof of chats indicating purpose of payment. They never replied and the deadline has passed with my account still active and without issues.
It is very hard to say in advance what will happen, exchanges can do what they please. It is not a good thing, but it is what we have. I've also had some unexpected issues over the years.
Your post sounds like contracting itself, and I don't know how did you feel that payment is from mixers like you wrote. Honestly, except if I am working for a mixer company in a signature campaign or any marketing programs for them, I never know if I am receiving my payment from a mixer. In case you are working directly for a mixer, it's more stupid to receive payment directly to your CEX account.
You are the one who is wrong. There are ways to know whether a transaction is originating from a mixer. It depends on the situation. With some mixers of the past it was obvious because of the structure of the transaction. These days you can also use tools to check if it is flagged as coming from a mixer.