When you choose to display your search results with the ajax search theme delivered with the plugin, several things happen.
Wpsolr creates a search page “search-wpsolr”, which only content is a WordPress shortcode. See Is there a shortcode to display the ajax search where I need ?
The standard WordPress filter ‘get_search_form’ is intercepted to replace your theme’s default search boxes with wpsolr’s search box.
add_filter('get_search_form', 'solr_search_form' );
The wpsolr’s search box form’s target url is then set to to the new page “search-wpsolr”.