If the person who created the ticket responds to the email they receive, the message is then appended to the original ticket as expected. The problem seems to only happen if an agent belonging to a team replies to the email they receive for a ticket created by someone else.
As a test, I also created a new ticket for a category that is auto assigned to a team that I am also a part of. If I reply to either email I receive (new ticket & ticket assigned to your team) appending to the original ticket works properly.