How to provide theme override for stylesheet conditionally included by a module
You can do this by implementing hook_css_alter as follows:

/**
 * Implements hook_css_alter().
 */
function mytheme_css_alter(&amp;$css) {
  if (isset($css['tiles-styles.css'])) {
    $css['tiles-styles.css']['data'] = drupal_get_path('theme', 'mytheme')
                                       . '/css/tiles-styles.css';
  }
}