Exposed filters submit with AJAX not working - regular submit instead
Found a solution. Ambidex idea is the key. My problem was that I didn't have printer classess within views-view--XXXX.tpl.php. After this everything works OK and there is something like "view-dom-id-82374yrcnuerhnw875yt3o8743y" (first line of Ambidex code) class added, which is probably needed by AJAX calls.