Nope. They never touch.
The domes and affixed projectors continuously rotate around a fixed point at a constant speed during normal operations. Each car arrives at the same speed as the dome rotates, and the arm basically pokes each bench into the dome and holds it in place, moving along the track at the same speed the dome rotates. At the end of the sequence the Kuka pulls the bench out of the dome and the empty dome then completes its rotation as it collects the next car.
Very much a modern day version of the original Journey into Imagination turntable arrangement.