I have set up a specific email address as a target that receives email notifications when an update is made to a ticket. When the recipient of that target replies to the email notification, a new ticket is created, rather than having their reply threaded to the original ticket. I would expect their reply to be added as an entry to the original ticket that the notification was sent from.
Why do replies to email-target notifications create a new ticket? How can I ensure customer email replies are added to the first ticket instead of creating a new ticket?
The target notification system is not designed to thread to an existing ticket and it is expected behavior that a new ticket would be created.
To allow this end user's email replies to thread to the original ticket (instead of creating a new ticket), you will want to stop using targets as your notification method. Instead, you should CC the end-user to your ticket so that they receive the CC notification. If they reply to that notification, their reply is added to the ticket as a public comment.
See Configuring CC permissions and notifications for more information on how you can customize your CC notification settings.
Ontec has authored a paid app in our Marketplace that allows you to forward entire ticket conversations (including private comments) to any external email. When the recipient replies to the forwarded email, their comment gets threaded to the original ticket as a private comment.