Hi Vlad,
I am really sorry for the delay of this reply.
I've checked your site and it seems like you have disabled "event applications" for users from your backend > easysocial > applications > event - user,
http://screencast.com/t/z8j4Duj6 hence the stream or any other related activity will not get processed. I've enabled back the applications and the stream is showing correctly now on user's dashboard.
Please have a look.