My opponent used Vertical Push on my Brewmaster. My Brewmaster landed next to an opponent's Aspect of Chaos. The turn that it landed, it was able to disengage, even though it became engaged that turn.
VP says "after 3 turns" which means that it actually happens at the end of the third turn, not the beginning of the 4th; you can tell because the champion generates AP after it comes into play, which means that it passes through a start-of-turn step. As a result, Brewmaster technically became engaged on the previous turn.
Interesting interaction. Props to you Kalasle, coming in again with your mad game mechanics knowledge XD.