Each time that I do the main story roulette and there's someone new, if I see that they are watching the cutscenes I politely ask the rest of the team to wait after explaining them that:
1) We're doing that roulette because we want. There's plenty of alternatives to get the same tomestones in the same (or less) time, without disturbing someone trying to enjoy the story.
2) If we need these specific tomestones, we're getting additional ones due to the new players. That's a whole other run that we don't need to do to get them.
If they proceed to ignore me, I simply wait with the new players (out of the boss room, or to guide them if they get lost somewhere else, like with the magitek). At this point the additonal dps/healer/tank is not needed, but at least I'm doing what I feel is right. I simply can't bear to see the new players' experience ruined because someone can't wait on the dungeon that they voluntarily joined out of the other alternatives that there's to get the very same tomestones. Ruining their experience on top of getting an extra thanks to them is just rude and selfish, especially when you run those dungeons because you want.
But I'm not that naive to not see that these rude players run that roulette just because of that reason (potential additional tomestones), and couldn't care less about someone else. They just want to finish it ASAP and f*ck everyone else. That, or they're just stupid and didn't notice that they don't need to run that.
By the way, it's not just the cutscenes what they get ruined, and thus the context of the whole dungeon (thus getting spoiled once they try to run it again or watch the cutscenes at the inn), but also boss fights or fun mechanics like the magitek mount part.
There's no excuse. When I don't want to wait I don't join the main story roulette, and I do something else.
P.S.: I also vote to perma ban people like the asshole that purposely spoiled the story on the OP's run.