I seems to you figured out how to get auto-opped cause the ~ is instead of the @, in Mirc you don’t see your @ only the ~, it means you are the roomowner.

Further in your java-webbased chatroom you get auto-opped because you have probably the advanced chatroom code. In mirc there is no where given your password so it won’t op you automatically. So that’s why you have to use the /cs op command.