You are incorrect. Of over 20 times that I got duty invite during dialogue/cutscene it was only twice that I was unable to commence. All other times, you are summoned into the dungeon and later find yourself standing in front of the NPC that initiates the dialogue/cutscene.

This works for 90% of dialogues, cutscenes and even cinematic-type cutscenes that involve custom animations and such.

Of the two times I WASN'T allowed to commence - both times make absolutely no sense. They were the simplest of dialogues, where the camera doesn't even move.

TLDR: 90% of cutscenes allow you to commence into a duty.