Well, I think I managed to find a solution. It basically changes the ajax url every time to the correct one. I’ve changed the search code to do that.
However you can’t place hovering styled result above the search bar. But if you use the results shorcode, you can place it wherever you want. (but it will display as a block, thus pushing the content) There is more info about this in the documentation: http://wpdreams.gitbooks.io/ajax-search-pro-documentation/content/getting_started/custom_result_box_position.html