Hi,
Okay, I think I see the issue there, something I missed previously. That is not the actual results page, but just simple page with a custom post carousel/content section. The plugin cannot pass it’s results there, as there is probably a completely different query that the section uses to get the results.
The default results page works differently, as it uses an internal WordPress query to simply display the results as required, and the search can connect to that query via the API an override the results.
This might be only possible via extensive custom coding to somehow connect the two different solutions unfortunately.