An interesting request. Thanks for raising it here. Site24x7's Alerting Engine notifies the 3rd party system and send the alert mail in parallel today. It would be difficult to add the ticket url the first time.
We'll check how we can support it in the product. One possibility is to notify back once we receive the ticketid and add it in the Alarms page in the product and optionally notify the technician.
Just curious to know if JIRA sends any notification to your Operations team once the ticket is generated..