The Duty starts 1 hour before scheduled departure, so if there is delay before first sector it's included in duty time.
Flight period starts with first off-block so if there was same kind of delay it was not included.
I worked with both systems. In the second one management didn't care to delay my pick-up if delay was before first departure. They only cared about disruptions enroute.
It was not long range ops, but 3rd world country with an old (1969) regulation.