The search bar on the video is not the Ajax Search Pro search bar. Make sure to replace it with the plugins shortcode or the module, that will solve the issue.
To get the best possible performance, please check this documentation, it has valuable tips on how to get the maximum speed.
In your case however the server back-end might need some optimization, as it takes me over 50 seconds to load the settings. That is unfortunately super slow, it should be at 2-3 seconds at worst, so it looks like the server is very overloaded.