There are multiple ways of notifying the end user when getting a response from an agent. By default, when you click into the box at the end of a ticket, this is going to create a NOTE. This NOTE will NOT send out an email to the customer/user out of the box. You can create a trigger to send that NOTE to the customer/user after one is saved to the ticket but I personally wouldn’t recommend that.
I think what you are after is simply responding to a ticket with the appropriate method outline in this article: Following Up — Zammad User Documentation documentation
Hopefully that helps. If not, please expand on exactly the work flow you are expecting.