Hi!
It appears that it’s not a javascript or theme related issue, as the plugin is functioning, but not returning results. I was not able to log-in with the details, but I believe this is a configuration problem.
From what I can see only posts are selected to search for, but I guess there are no posts to return? Maybe you want to search products or pages? In that case make sure to select the custom post types to search for on the General Options -> Sources panel.