Binance was able to track the transfer, although I did not transfer directly from the mixer to the platform, but rather that all transfers were made from my own wallet. The means of tracking on the blockchain have evolved to the point where it is really difficult to hide completely. Yomix Mixer should take into consideration these details.
Does this mean you mix some coins, transfer them back to your wallet, and then send some coins to Binance? They might flag them since your previous transactions are related to conjoin transactions. I recall reading something like this in the past, saying that Binance will check your previous 5 related transactions to see if they are "suspicious". So, as long as you use a new address from mixing your coins, the chance that they would detect your mixed coins would be smaller, albeit not impossible since everything is on the blockchain. It is also a good practice to never send back your mixed coins to your own wallet, and just use the new address/wallet entirely. CMIIW. Pretty sure any decent mixer would consider this when they built their platform.
If the worst comes to worst, using DEX would be a good idea to swap your BTC after doing some mixing. Or just drop centralized exchange entirely if you don't want to deal with their false flag regardless if you use a mixer or not. Improving your privacy practice would be a good idea too.
Centralized exchange have the required tools to track transfer done on it either for good or bad, but with disclosed entity. Binance is the largest crypto exchange that stores coins and having one of the top trading volumes of crypto currency. Although it was hacked last year and the CEO of Binance, Changpeng Zhao reinforce his team to encrypt and decrypt data of users of the exchange. The exchange security is improving on a daily basis and reducing the scams to its minimal rate but it can not be eradicated totally.
They can definitely collect any data related to mixers by doing something like using the mixer on their own to collect some addresses and so on. That being said, I don't see them being hacked or whatnot related to their ability to track/link coinjoin/mixer-related transactions.