Plugin sorting overrides sticky post option

What result template you are using?
This is a rather tricky problem, do you want to show the sticky post even they are not in the search result? Or, you want to show the sticky post when they are searched?

I am using the default (not ajax), sorting by post title. The sticky post is actually within the results, but it takes it’s place with the set sorting by post title (by alphabetical order). I need it to show at the top of the list (as it’s sticky and should show at the beginning by definition)

Here is an example:
if you click this link
https://thedogsnetwork.com/category/pet-friendly-restaurants-cafes/
This is the archive for pet friendly restaurants. I have set La Pina restaurant to be sticky, hence it shows at the beginning.
But if you use wpqsf from this page: https://thedogsnetwork.com/find-a-pet-friendly-restaurant/ to generate those results: https://goo.gl/cQc9pu
You will find that La Pina is not at the beginning of the list as it should be. It shows on page 2 of the results, by alphabetical order.

I want it show at the top as a sticky post when searched

It’s still not clear.

There are two situations here:
1. Show sticky post on top regardless the searched result.
– This is when the searched results does not have the sticky posts, but you still want to show it at the top of the result.

2. Show sticky posts on top only when they are in the searched results.
– This is when there are sticky posts in the searched result and you want it to display them first.

Note that these two situations have complete different solution. And situation number 2 is more complicated, it required you to know php for customization as the coding is theme dependent and I can only guide you how to do.

OK, I can settle now for option #1. Can you tell me how to do it? (showing sticky post on top regardless what the searched result is)

Well it is actually out of this plugin support.
But you can try to add these codes to your search.php:

<?php
$sticky = get_option( 'sticky_posts' );
rsort( $sticky ); // Sort the sticky post with the newest ones at the top
$sticky_posts = new WP_Query( array( 'post__in' => $sticky, 'ignore_sticky_posts' => 1 ) );
if ( $sticky_posts->have_posts() ) {
	$return .= '<ul>';
	while ( $sticky_posts->have_posts() ) {
		$sticky_posts->the_post();
                //here display your sticky post
		$return .= '<li><a href="' .get_permalink(). '" title="'  . get_the_title() . '">' . get_the_title() . '</a><br />' . get_the_excerpt(). '</li>';

	}
	$return .= '</ul>';

}
/* Restore original Post Data */
wp_reset_postdata();
?>

Note that you MUST have sticky post before you can use these code.

PS: If you have further question regarding sticky post, please ask for help in the related forum.