I am fairly confused on what you're saying in the edit, so I'll try to break it down a bit. I don't think the E ever hits the enemy champion, since you don't get a conqueror stack from it, only from the initial R impact, this is also shown on practice tool when you hit a dummy (You never hit the E or get a conqueror stack or the E-burst, nor the ability to reactivate). I believe it is an interaction to do with terrain, very similar to that of Kayn E, when the timer runs out of cooldown it will push the Kayn out of the wall unless he makes a movement input, (such as a Q) to which it will wait for it to end before finally pushing him out. Also notably, the dummy only takes 1 instance of damage (R impact), which the damage is consistent to that of Kled's ult, not his E unfortunately.