In Control Panel/Member Management/Edit Profile/Preferences

This feature is not working for me.

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When you say not working, What does that mean?
Possibly you have a file permission issue in your admin folders.
Or could it be that you are logged in as the admin?
If that is true the Island will show invisible, But when you select the details they become visible. But that is because of you are a admin.

No, it is about users too, not just admins or moderators, anyway if this option there it should be available for Admins, am I right?

I still don't understand what your problem is, what are you trying to do?
There are other settings for this feature.

Control Panel » Display Options[+]Who's Online
Disallow Invisibility:
Prevent users from choosing to not appear as online at any time.

Control Panel » Site Permissions
Can See Extra User Info