Hm. I think Yun's escape spot is not the same lift, so the two events can coexist. Yun is lifted up much closer to the opposite end of the room, where Kyle starts: in the cutscene Kyle turns (theoretically, to the lift from where Yun came) to face the stormtroopers. I believe the Stormtroopers used the same lift Yun used at the start, descending from above, and it's not the same that Yun uses in the escape. Level 7:
Level 8: