The easiest, and most useful instance to demonstrate this cross up is after a knock down with Jinrai. If Ken is 1P, then after landing Jinrai he super jumps towards his opponent without attacking, he will cross them up as he lands right as his opponent is getting up. Ken sort of lands right on top of them so it is hard to figure out what side Ken landed on until it is too late and he’s strong fierce supering you. Now here is the really weird thing about this. If 1P Ken hesitates for just a split second, and then super jumps, he will not cross up. He will land on top of them again as they are getting up, but this time still be on the same side he jumped from. Again it is too fast for your opponent to see and if they were expecting the cross up, they will surely get hit by this non-cross up jump in.
The confusing thing about all of this is, 2P Ken works totally differently. 2P will never cross up. He always lands on the same side that he jumped from. What is different between the two sides mid screen I have no idea, but something is different. 1P Ken will cross up if you jump early, and not cross up if you hesitate and jump. 2P Ken on the other hand will always not cross up. 1P Ken obviously got the better deal out of this, giving him a really good mix up on wake up after a super. I’ve hit so many people with this by mixing up when I jump. It seems like no one really knows about this, so it’s a 50/50 guess for your opponent in your favor.
On characters Ken can do this to, especially against shotos and Chun Li, he should always pick 1P side. The slight difference in time between crossing up and not is really small, and most people probably don’t know about it to begin with, so knocking someone down with a Jinrai can lead to another super almost for free.