This video really helps to explain things even better. Be sure to watch the whole thing... but I am going to link the video right to the part I am talking about... 3:04 in the video...
In particular... the part about the below image in the video...
The style of twisting that we are talking about really does exactly what the above explains. See below...
Kenzo Shirai tumbling video:
Kenzo take off example #1 (1.09 in the video)...
Kenzo take off example #2 (1:27 in the video)...
In both of the above videos you will see the contact twist combined with the tilt twist. The drop arm is brought forward to remain in the "twist plane" as the video describes.
Again... one arm out to the forward side and one punching up. So you basically have an arms to the side with one pulling down and in and one punching up and in.