No Emails sent on User Creation in D8 through Rest API
I've tested this and it seems like _user_mail_notify just isn't working currently in 8.2.4, however I did find a workaround using the hook_ENTITY_TYPE_insert() still, but using hook_mail and MailManager also.

/**
 * Implements hook_mail().
 */
function custom_rules_mail($key, &amp;$message, $params) {
$options = array(
    'langcode' =&gt; $message['langcode'],
);
 switch ($key) {

   case 'create_user':
     $message['from'] = \Drupal::config('system.site')-&gt;get('mail');
     $message['subject'] = t('Welcome to the site!', $options);
     $message['body'][] = $params['message'];
     break;
 }
}

/**
 * Implements hook_ENTITY_TYPE_insert().
 * When a new user is created, do things.
 */
function custom_rules_user_insert(Drupal\Core\Entity\EntityInterface $entity)
{
  global $user;

//  _user_mail_notify('register_no_approval_required', $entity);


  $mailManager = \Drupal::service('plugin.manager.mail');
  $module = 'custom_rules';
  $key = 'create_user';
  $to = $entity-&gt;getEmail();
  $params['message'] = "Welcome to our site! \r\nYour username is " . $entity-&gt;getUsername() . " " . "\r\nIf you would like to reset your password, you can at the following link: \r\n" . user_pass_reset_url($entity);
  $langcode = $entity-&gt;getPreferredLangcode();
  $send = true;

  $result = $mailManager-&gt;mail($module, $key, $to, $langcode, $params, NULL, $send);
  if ($result['result'] !== true) {
    drupal_set_message(t('There was a problem sending your message and it was not sent.'), 'error');
  }
  else {
    drupal_set_message(t('Your message has been sent.'));
  }

}


The way I have this set up works. When a user is created (through drupal GUI or REST API), they are sent a welcome email that also includes a link to reset their password. To do this, you use the user_pass_reset_url function that is defined here. MailManager was pretty simple to use and figure out.

I followed this blog to figure out how to do this.