You do see that users activity. I just described that's exactly how it works. Your test user has no activity. So there's nothing to display. Look at your admins profile as your test user and you'll see that admins activity, because they have activity.

Showing your connections activity on your profile for other viewing users makes no sense and isn't how any of the other social site functions unless you have been tagged in the activity or the activity has been posted to your stream directly. Tagging isn't implemented yet, but I'm working on it. Posting to another users stream directly is implemented. To test this go to your test users profile as your admin and post on their wall. Now login as a different test user and you'll see the admins post on your first test users wall.

If User A visits User B then User A will not see the connection activity of User B. If User B visits his own profile then he will see the activity of himself and his connections. User A will only see the connection activity of User B unless a connection has posted directly on User B stream. This is exactly how Facebook, Google+, etc.. all function.

The module behaves like Recent Activity The tab functions as described above. This behavior is hardcoded in and there are no plans for a parameter to change it. You'd need to modify the core stream code and change how a stream source behaves.

You can also render the profile activity in a module by substituting in the tab using CB Content Module; as it's entirely AJAX driven this should work fine.