I don't like doing it towards my hand therefore I do it like the 1st vidI do it like the second video.
But I dont think it does matter, the result is the same.
In movies and such you see cooks make a sport out of it to steel as fast as possible.
I think its more important to try to hit the same angle as you did on you stone.
Therefor use the steel very very slowly. Its so easy to overangle and create an huge new (micro)bevel.
Also, a few passes per side should do the trick. If you need more, thern you are just forcing a new bevel on the edge, which of coarse makes it sharp again. But you have to grind that out the next time you sharpen on the stones.
I do it slowly as well and with a light touch and always focus on the angle to not use too high of an angle