BuddyPress.org

Good question. Selecting an option in the drop-down fires off an ajax query. Look at the section under the “List tabs event delegation” comment in global.js; that calls bp_activity_request() which results in the ‘wp_ajax_activity_widget_filter’ action being called, which regenerates that section of the page.
If you look in activity/activity-loop.php, look at the call to bp_ajax_querystring() in the bp_has_activities() call; that’s the part that passes the user’s option cookies to the templatetag.

I hope that’s what you were after!