How to make sure simpleSamlAuth module is working as intended?
There are hooks and config in the module UI that should aid in this. Here is an example from a Drupal 8 project I did that does just this:

/**
 * Implements hook_simplesamlphp_auth_allow_login().
 */
function MYMODULE_simplesamlphp_auth_allow_login(array $attributes) : bool {
  // Debugging purposes
  \Drupal::logger('mymodule')-&gt;log('info', 'Attributes contained: @attributes', ['@attributes' =&gt; $attributes]);

  if (empty($attributes['EMAIL_ATTRIBUTE_IDENTIFIER'])) {
    \Drupal::logger('mymodule')-&gt;log('info', 'Attribute was not present.', ['@attributes' =&gt; $attributes]);
    return FALSE;
  }

  // Run a query to see if the user exists by email address in Drupal
  $exists = // query users by email address

  return $exists;
}


Perhaps a simpler approach in your case would be hook_form_alter, adding a new submit handler and doing the email check there before anything else happens, but the hook above is the final say-so in if a user can authenticate and login or not.