Since enabling comment moderation on the Tavern, I’ve discovered that WordPress does not notify commenters when their comments are approved.
On the Tavern, I’m using the Comment Approved plugin by Niels van Renselaar. It allows me to create a custom notification message that is sent when a comment is approved. Unfortunately, I don’t think it’s working. Please let me know if you’ve received any comment approval emails from the Tavern.
I strongly believe this feature should be in core. I’ve started the process by creating a feature request ticket on WordPress trac. Let’s discuss the pros and cons or why you think it shouldn’t be in core. Please give me your feedback in the comments or within the ticket.
The plugin is not working for you because you’re using the Jetpack comment form.
The Comment Approved plugin adds a checkbox to the normal comment form, which says “Notify me by email when my comment gets approved”. This checkbox does not appear on the Jetpack form, because the Jetpack form replaces the normal comment form. So, that setting is never checked for anybody, so nobody gets a notification.
You can use Jetpack comments, or plugins that expect you to be using normal comments. Not both.