All I have to say is if you ever jumped over a bush with a stick you would know that it would not occur to you to push the stick, but rather pull on it.
I have been jumping over things with sticks since I was five years old, including but not limited to bushes, puddles, creeks, truck hoods, hay stacks, barbed wire fences, and fiberglass bars. If an athlete is stiff poling with their hands separated normally, the pull must come primarily through the top arm. The bottom arm is too close to the body to pull effectively. This is why the great stiff pole vaulters slid their hands together so that they almost touched as they left the ground. This allowed them to pull with both arms instead of being limited to the right arm alone. I maintain - and the illustration with the gymnast on the rings that you did not understand was meant to illustrate - that the left arm must be above the head if it is going to be of any practical use in pulling on the pole.
So you insist on pushing a pole for a tenth of a second or perhaps 0.0765 of a second. How do you figure how long to push.
What is the purpose of the push in the first place? Can you answer that?
I know that no one can think in terms of timing parsed to such thin margins. Awareness of the need to pull with the bottom arm and awareness of the position the arm has to be in to perform that function is all that is necessary to have the kinesthetic awareness to keep the pole from hitting you in the head at takeoff. Fee takeoff or not, completely collapsing the left arm is not optimal, nor is pushing on the pole in such a way that it inhibits other aspects of the jump.
The purpose of the push in the first place is to keep the left hand high enough above the head that the muscles of the upper back and shoulder can be used to pull. I'm sorry if I did not make that clear earlier.
The reason it was touching the head in the first place was precisely because he did not push the pole at all.
My point exactly. He did not push at all; his left arm collapsed at takeoff, and he jumped very high. Then his left arm stopped collapsing, and he jumped even higher. You speculate that there must have been a flaw in his takeoff that was later corrected. I speculate that he began to push a little on the pole just as he completed the free takeoff, thus maintaining the advantage of the free takeoff while keeping his left arm in a position to pull.