Maybe this is a bug or maybe I just don't understand the intended behavior.
When someone creates a Reminder with me and the Owner I get an email notifying me that a 'ticket was created'. Great, everything is working properly. The email I receive has a helpful link to the Ticket. This is the 'Reminder Ticket', and not the ticket where the Reminder was created. I guess you may call this the Parent, though though the relationship is not shown in Links. Everything is still great. If I click that link and Resolve or Quick Resolve the Reminder Ticket, the Parent Ticket History does not show the Reminder as 'completed'. This is not very great and is not the behavior I expected. The History does show that the Reminder was created, but that is only half of the story. This behavior is different than what happens when you select the checkbox to 'complete the reminder' on the ticket, which does log the completed reminder in the history.