Solution:
If you are using custom registration form, you can send the email before updating the database.
add_action( 'user_register', array( $this, 'user_register' ) );
function user_register( $user_id ) {
$billing_company = $_POST['billing_company'];
wp_mail( $email, $subj, $billing_company, $headers );
}
Alternatively, you can delay the execution of the function with sleep:
add_action( 'user_register', array( $this, 'user_register' ) );
function user_register( $user_id ) {
sleep(5);
$this->send_notification( 'admin-user', $user_id );
}