Many exchanges believe that if a coin came from a mixer, it must be tainted, regardless of its origin. That's why what you quoted is important. NotATether, Thormixer and Jambler's partners have a very functional model, so even various AML checkers cannot recognize that the coins were part of the mixing process at all.
That's true, the coins that come directly from mixers have been considered tainted by the exchanges and when I used to be part of a mixer campaign at Bitcoin and receive my weekly earnings to my exchange account directly instead of first receiving those at my own addresses then moving those at exchange's address, and for that I faced some issues.
When it comes to Thormixer, and Jambler's partners I can surely say that I've deposited the mixed coins at my exchange's address and I faced no issue or warnings at all. And, that's why I believe the coins that get mixed using Thormixer or any of Jambler's partners are clean coins not tainted ones.
Exchanges can only become weary of bitcoin coming into their exchange if they can not trace the source from which or where it's coming from, so in other words, exchanges can only know that the bitcoin coming into the exchange was mixed, only if the person or user mixing the bitcoin made the mistake of submitting a direct Exchange bitcoin wallet address for the mixed coins to be sent there right from the mixer, this is usually a huge mistake ..
Mixed bitcoin should first be received on one's personal wallet, and after some time, the person can then send the bitcoin to the exchange wallet address, there won't be any issue of tainted coins .