There is no such thing as Monero Mixers or Tumblers. Such a service would be a waste of money and time. Monero is inherently Privacy oriented and offers a private way of handling funds. No body can see where your XMR comes from or whose address it went to.
LocalMonero is simply a platform that allows you to trade Coins. If you ever hear some body promoting a Monero Mixer. It is most probably a scam.
-----
But it is not perfect anonymity. The transaction fees and timestamps are still visible and so if you withdraw Monero from an exchange, they can match up that withdrawal with a transaction on the blockchain using the timing and fees as clues. They cannot follow the money after that initial transaction though, unless you transfer the coins to another centralized exchange. So Monero offers more privacy than other cryptocurrencies, but moving coins between your own wallets is better than going through exchanges if you want to stay totally anonymous.
They can match time stamps but they can stick that up their bum because there is no better thing they can do with that information. You transfer the Coins to another Centralized Exchange and the first Exchange will not even notice. No body else will either.
Anyway. What is the point of even using Monero if all I am doing is moving Centralized Exchange funds to personal Wallet and then back to another Centralized Exchange. It is pointless and useless.