I noticed that I made a mistake I had "Stream post URL security” turned on. But I also had to recreate the facebook channel in order to sort out authorization, Now it works, but there still is one problem I don't quite understand. Posts get published in "visitors posts" area of the facebook page instead of main timeline. Creator of the facebook app is also administrator on that facebook page.
Concerning to Posts published as "visitors posts" instead of the Page itself. it may be related with the last published version for Facebook API 2.4. Please, download AutoTweetNG Free 7.9.4 and update your site again (previous update may have failed to copy all files):