You can use this code to automatically send an email whenever a post of the type one is published. This goes into your theme’s functions.php :
<?php
function post_published_notification( $ID, $post ) {
$type = get_post_type($ID);
if ($type == 'post-type-one'){
$author = $post->post_author; /* Post author ID. */
$name = get_the_author_meta( 'display_name', $author );
$email = get_the_author_meta( 'user_email', $author );
$title = $post->post_title;
$permalink = get_permalink( $ID );
$edit = get_edit_post_link( $ID, '' );
$to[] = sprintf( '%s <%s>', $name, $email );
$subject = sprintf( 'Published: %s', $title );
$message = sprintf ('%s, Your article “%s” has been published.' . "\n\n", $name, $title );
$message .= sprintf( 'View: %s', $permalink );
$headers[] = '';
wp_mail( $to, $subject, $message, $headers );
}
}
add_action( 'publish_post', 'post_published_notification', 10, 2 );
?>
You can read and the code and modify the parts that you want, depending on your needs. I could post a more accurate answer if your question was clear. However, the function itself is pretty explanatory.