1:55: "... vibration is done by the arm of the man ...." So it's okay for the man to jerk the lady around with his arms now? Yuck. I don't doubt that Bosco and Pitton are accurately describing the WDSF style there, but if so, it sounds like a singularly uncomfortable style.
....and because I just can't seem to help myself, I found a clip of Paolo and Silvia demonstrating a Tango Progressive Link in which they mention the concept of Sudden Movement....
Not much help to me about the mechanics of the "how".
This seems to confirm to me my unvoiced hypothesis about what the concept corresponds to in classical English style - roughly, "WDC style" in current WDSF parlance. Since this is the Geekery thread, I'll go into some detail. In the process I'll try to address two different versions of "how".
In the example of the tango link, the classical approach, using the classical English ballroom tango hold that wraps the right arm around the lady with the forearm diagonally down the lady's back ending with the man's right fingertips at roughly the lady's spine at the small of her back, the crisp action is produced by use of a "head snap", which I will describe. Note that the classical tango hold is different from the WDSF tango hold, which is wider with the man's right arm less around the lady's back, and also from the Argentine hold, where the man's right arm seems to go more around the lady's back, well across the spine, if I'm correct about what the Argentine tango folks are doing.
From the leader's point of view, the head snap consists of first, a small windup of the head to the right, then a sudden movement of the head well to the left, to promenade position. The directions "right" and "left" describe both head turn and, to a lesser extent, head and neck - cervical spine - tilt. The rotation of the head to the left accompanies a rotation of the hips and feet to the left - toes go with the nose - and an accompanying rotation of the shoulders and rib cage to the right. This should in turn lead the follower to turn head and hips to the right, ending in a promenade position where the rib cage and shoulders are still parallel to the leader's, while the hips are open to the leader's left - follower's right - in approximately a 90 degree V, 45 degrees in each partner between hips and rib cage.
Now, this will lead a crisp, sharp turn to promenade in the follower in the classical tango hold. However, in the WDSF tango hold, I think because of the different locations and angles of the spine, it will give the follower whiplash. The WDSF solution to this appears, based on your videos, to be to transmit the impetus from the leader's head windup and turn to the follower through the frame and arms rather than through the body and body rotation. This incidentally results in the rib cages and shoulders turning with the hips to some intermediate angle, the entire "body" of each partner turning slightly to form a narrow V rather than there being differential turn in the rib cage and hips to parallel shoulders and a less narrow V in the hips.
I would assume that the Argentine folks don't use any of the "head snap" nor "sudden movement" stuff, but they should feel free to correct me if I'm wrong about that.