Hi!
Well, the closes thing you could do is to redirect the results to the results page when clicking the magnifier or return buttons, with results override activated, as it is not possible push them to a separate page.
On the results page, you could also place the same search instance shortcode/widget, and enable the live results loader feature. I have looked at your themes results page source, in your case the container selector needs to be changed to:
[html]#content-area[/html]
..here, like so: https://i.imgur.com/SElhVcY.png
In that case, whenever the plugin detects, that it is currently on the results page, it will use the live reload feature. When the override is enabled, the filter states and the phrase is also memorized and sent to the results page search bar.