Agent not receiving notification on comment made by customer

Agent not receiving notification on comment made by customer

I have turned on notifications on Adding/Editing/Deleting a comment. When agent makes a comment, the customer gets a notification. But when the customer comments, the agent is not getting a notification.
Agent gets notification only when the customer uses the Reply button. But it is confusing. Why is the customer given two ways to send replies? They will mistakenly add a comment and the agent will never know.