If you could email me your website at email@example.com so I can debug I can better assist you with the issue. It can be a compatibility problem with another facebook plugin. Make sure that all facebook plugins use the same application ID and the application is set up correctly (as shown in the the tutorial).
Secondly, I think you misperceived how the premium plugin functions. On the sales page the function is described as:
"When a user clicks on the 'like' button, it won't show for subsequent visits (free api key needed). This system works with cookies (visitors need to click the button and login once, if cookies are cleared). It cannot check if a user is a fan or not, no plugin can without authorization."
please contact me back on this forum or at firstname.lastname@example.org (the dedicated support email), whichever method you prefer to contact us).
We are sorry for the inconvience and hop to provide a solution/fix for this issue