How to Rebuild Registry On Admin Form Submit
In order to fire a submit callback you have to add it to #submit array within your form. Here is an example.

/**
 * Form builder.
 */
function my_admin_interface($form, $form_state) {
  $form['#submit'][] = 'my_admin_interface_submit';
  return system_settings_form($form);
}

/**
 * Submit handler.
 */
function my_admin_interface_submit($form, $form_state) {
  drupal_set_message(t('Hey there!'));
}


Here is a link to the manual.