This service is different than the rest due to this chip feature, which is, essentially, funds deposited prior your decision to mix coins. This means that it's time which makes it hard to trace. If you knew that I wanted to mix within a certain chronological period, you could exclude lots of transactions to detect who's the mixer.
I just don't understand how you know when it's the perfect time to create new chips.
When someone deposits bitcoin to their service, they must withdraw within a certain time by obtaining a private key for the various chips they have. Once a private key has been given to a user, CM knows that chip is no longer available and can update their database. When someone withdraws a chip, they will not necessarily spend the UTXO immidiately.
CM can periodically create new chips in a number that is approximately equal to the amount of chips that have been withdrawn. They can also estimate demand for their chips based on current account balances, and use their profits to create additional chips of certain sizes.
Generally speaking, it will never be a secret that a particular UTXO is from a particular mixer. Blockchain analysis companies will use mixers to trace that mixer's UTXO set.
From the looks of it, chips do not stay on CM for very long. One tx that CM used to create chips was 9146153f9c90075d781c3ac798472648f36e9849069a57e26206b9ca40e86e8f (12/27/2020) and the first output address was 1Mte55HMcubh11MNfKNk7C6mXjWnHj7vX It looks like whoever received this chip also received several other chips:
17c5d8ZpsEthDRaZqsCryM5kHqy1Vbc3cq 0.03200000 BTC (1/30/21)
14b47PAmGKsEGrvoZ9LpQdSvQbdKQ6QafJ 0.00200000 BTC (1/26/21)
157jeJakzkK18sayYsyfxKCGa8U1zrmPnb 0.01600000 BTC (1/31/21)
19xFcK3CLkUEBAC5PTfNHQN2rcEueFBexu 0.00200000 BTC (1/25/21)
1NQHAzip6EA3hBFjKPKgZTsvuKQmAW2pfC 0.00200000 BTC (1/27/21)
1Edu9FAbZXCFq3KXM5jgd4p2J1A1pSn9ci 0.01060600 BTC (1/7/21)
15GMbRgb63mYxBosA1CsKbTir9cNTDggjr 0.00008700 BTC (1/30/21)
16WgyvtAECWtDw4PpEqTQD8JYZ8y73pAyt 0.00800000 BTC (1/27/21)
The transaction that spent all of the above chips 186c9c1f6f6cd7b15a81c5836852fc3206e441583902adda18ad7a51242afe9c was confirmed 2/2/21. Whoever received the above chips cannot have received them prior to their funding date (noted above), nor after when they were spent (2/2/21). It is possible this person received chips from CM over time. I would say that the above transaction suggests CM holds chips for somewhere between 2 and 8 days before giving them to a customer.
So CM is creating new chips at a rate of at least once per week. Again, you should not expect the fact that you have a UTXO from CM to be a secret. Each of the above chips was funded with a transaction with exactly 20 outputs, all of which are exactly of the same amount (there is no change address).