Emailing Authors only when a CUSTOM POST TYPE post is published- not when edited later [duplicate]

Question

Yes, it sounds like you do want a post transition hook, probably draft_to_publish as per the following from the Codex:

function your_callback( $post ) {
    // Code here
}
add_action( 'draft_to_publish', 'your_callback' );

Use authorNotification— your function name– instead of your_callback. It should be fairly simple in your case.

However, the precise details of your project are not clear. You may require something more complex. I can’t tell.