Hi Attila,
Thank you for all the details, it helps us a lot.
So, I have looked up the given review on the review editor screen, and the permalink of that review is the same as the plugin is returning (without the ?r=s argument): https://i.imgur.com/BxTKrT6.png
If you wish to add that string to the results, it is possible via a custom code. Try adding this custom code to the functions.php in your theme/child theme directory. Before editing, please make sure to have a full site back-up just in case!
add_filter( 'asp_results', 'asp_custom_link_results', 10, 1 );
function asp_custom_link_results( $results ) {
foreach ($results as $k=>$v) {
$results[$k]->link .= '?r=s';
}
return $results;
}
This should append the ?r=s part to the end of all results links.