There is no coinjoin coordination service offered by these phishing sites, they have complete access to your transaction data and complete custody of your coins.
As far as I know Bitlist never claimed any website is using coordinators.
Services you mentioned are calling this ''coinjoin'' on their website, even if it's not a real coinjoin with centralized coordinators like you.
I wouldn't go so far to calling them a phishing websites, and I didn't know word coinjoin is trademarked.