External email is what i use to send out emails to the user after they send one to me.
The initial setting is setting the reporter to the email and they are a watcher.
When they send emails back, they don't get an email with their comment which is good.
If another agent wants to send an internal comment, then the external email gets an email of it too. It shouldn't do that. If I remove the external email from the reporter or the watcher, then they'll get emails for their comments.
Ensure that they won't get internal comments and that they won't get emails with their own comment.