Hi Steven,
The results page is a built-in WordPress feature, and is always handled by the currently active theme. Ajax Search Pro can not change the results page, as it is a WordPress core feature handled by the active theme.
The results page is invoked, whenever the “s” query argument is present in the URL, for example “www.yoursite.com?s=phrase”. When that is detected, WordPress tells the theme to display the search results.
All our plugin does by default is redirecting to that results page. When the search results override feature is also enabled, it will also tell the WordPress core which results to display on the results page.
The layout of the page, the functionality etc.. all depends on the currently active theme. Some themes also have support for page builder plugins, like Visual Composer, Elementor Pro or similar, which can help you customize the results page layout.