Apart from the default New ticket email notification, there might a Dispatch'r rule that's sending an email every time a new ticket is created. Please open the ticket from that requester and click on the Activities button to see if there was any Dispatch'r rule executed on that ticket.
You could navigate to the corresponding Dispatch'r rule by clicking on the rule link for that activity. From within the Dispatch'r rule, you could verify if the email notification is being sent, this would be available as an action within the rule. You could remove this action or add another action - "Skip new ticket email notification", to that Dispatch'r rule, which would prevent the email duplication in cases where this rule is triggered.