Suggested template file is not working for Custom Search's template
This is a known issue with the Custom Search module for Drupal 7. Of note from the issue:


  Copy custom_search/theme/custom_search-result.tpl.php to your theme
  location (e.g, sites/themes//templates/search-result.tpl.php), modify
  accordingly and then refresh your caches.
  
  Tested on the current stable - custom_search 7.x-1.11


The solution is to rename custom_search-result.tpl.php from the module to search-result.tpl.php in your theme.