gistfile1.php

function listing_published_send_email($post_id) {
   $post = get_post($post_id);
   $author = get_userdata($post->post_author);

   $message = "
      Hi ".$author->display_name.",
      Your listing, ".$post->post_title." has just been approved at ".get_permalink( $post_id ).". Well done!
   ";
   wp_mail($author->user_email, "Your job listing is online", $message);
}
add_action('publish_job_listing', 'listing_published_send_email');

You should know this action is triggered anytime when a published job is edited.

@kleampa this version should fix that: https://gist.github.com/danjjohnson/b6af263d896fb34f713a149edee45f52