Hello RussianBlue,
Sorry for late reply to this,
I make an sample explanation, let's say privacy site and public site
step 1 : copy that RSS FEED URL from the privacy site after you click the button
step 2 : GOTO your public site backend > easyblog > Feed importer > add new > paste the RSS FEED URL in the "Feed URL" field (
http://screencast.com/t/Kpr6TzrLout7 ) | And select your category and author (
http://screencast.com/t/xSuog6bj ) > then save
Step 3 : you have to set your cronjob for run this automatically when your privacy site publishing a blog post, so you no need to manually to run this URL in your public site ( http://yoursitename/index.php?option=com_easyblog&task=cronfeed ).
The Cron Feed documentation ->
http://stackideas.com/docs/easyblog/cronjobs/setting-up-cronjobs-for-feed-imports-in-cpanel
Hope this help.