The last two dungeons of the ARR launch story have about half an hour of cutscenes in them each. Most groups will not wait for people to watch them.
You can either :
a) Watch the scenes and be locked out of fights. Possibly have some scenes not trigger at all due to the group triggering later ones before it can play.
b)Skip the scenes and watch them later in the inn.
c) Make a premade party with Party Finder letting people know that you want to see the scenes and do the the fights. One or two 60 players can carry the instance unsynced.

SE learned from this experience and placed most cutscenes before and after dungeons instead of during from then on.