Wasabi is built in such a way that the client does not trust the server, and no sensitive personal information ever leaves your laptop.
This means the coordinator (with whom you agree to the T&C) does not know your IP address, name, or which addresses belong to you.
You only trust the coordinator with uptime, meaning that it is expected that some addresses might be rejected from registering. In this case still nobody can steal your bitcoin, and you can spend them wherever you want.