It's automatic after you exit out of your final path.
If ur doing a legends run then the title is a bit misleading, was it for taunting?
It automatically starts once you enter a heroic or master versions of the monthly event quest and stops once you complete them both 100%. There's no clock that tells you a time, it just gets submitted. Most people use a stop watch app to track their time on the side.I'll be honest, the times are very fast, and if you didn't complete them both in just a few hours... you won't have a chance. There's a handful of forum posts of people putting up their times for each month - check then out if you'd like to get a rough estimate on times.I'd focus on bigger and better things than a Legends title right now