If they are coordinating the coinjoin on servers they control then isn't it possible to know which output address belongs to who?
Good question, but coordinator wouldn't know which output belongs to whom because it uses Chaumian CoinJoin. Here's short explanation from Wasabi docs.
A Chaumian CoinJoin is a special type of CoinJoin that utilizes Chaumian [or Schnorr] blind signatures to prevent the central coordinator from spying on the linkage between inputs and outputs.
If you're interested with how it works in detail, check
https://github.com/zkSNACKs/WabiSabi or
https://docs.wasabiwallet.io/using-wasabi/CoinJoin.html#zerolink-protocol-step-by-stepAre we sure that Wasabi is using Chaumian CoinJoin? Could they be saying they are using Chaumian CoinJoin, but are using a different kind of coinjoin and recording which outputs belong to whom?