Hi Erwin,
By back-end you mean the preview area of the search plugin? If so, there is a disclaimer, that in preview mode some functions might not work correctly: http://i.imgur.com/wSGgqSG.png
If you mean the option search (“Can’t find an option?”), that is not an ajax search, but a client side text based search, and only affects the browser – it is not connected to the server, nor the database.