If I remember it correctly, somebody said their mixed coins were classified as tainted even though they already move them through some addresses. So some exchanges might trace back to more than just one past transaction to see if your coins are "bad" or not. Although if you use a mixer that doesn't really make it hard for exchanges to see that you use them is a bad idea to begin with.
Most of the TOS that exchanges are using specifically bans the usage of such services. However, the problem arises when you consider Bitcoin should be fungible.
Exchange can absolutely do so, but if you can prove beyond reasonable doubt that you weren't aware or otherwise associated with them, then it is fine. They have to actively prove that you are the one that is using it and you can use plausible deniability to your advantage. Afterall, they cannot prove that you were the one using the service unless you were to send it directly to your exchange without any hops.