Usually in HS for the next upcoming movie they'll show about a 5 min scene from the movie. Sometimes with an actor or 2 giving a little speech or some behind the scenes info. They've done this for a handful of movies.
At DS AMC, normally they don't do anything out of the ordinary. Maybe a pin but that's about it. It's pretty normal going. The only time they did something more was for the premiere of Rogue One. You bought a ticket that covered the movie then gave you access to an after hour Star Wars event at HS. Rides, fireworks, etc. They only did it that one time and not for the following Star Wars, so no telling if they'll ever do something like that again but I could see them doing something like that for Toy Story 4 with the new land