Oh I understood the vibration being a huge issue.
I was just curious about how the tripod used helped reduce the vibrations and if a similar tripod but a bit more affordable would give similar results. Are the materials that are used in the making of the tripod the main factor in helping reduce the vibrations? Or is it mostly the brand's tripod design that helps achieve the best results?
Is rigidity the best solution to reduce vibration? Or is dampening the vibration using weight centered under the tripod and carbon fiber the best solution?
Like all things, there are many opinions.
Some go so far to say a poor cheap tripod is worse than no tripod at all. I frankly cannot imagine that, any reasonable help is certainly some help. But more sturdy includes larger diameter legs, for example 1.25 inch diameter instead of 1.0 inch diameter (its in mm today). Which becomes heavy to carry of course. I don't think carbon fiber is more sturdy, but it is lighter, and does help to damp the vibration. Wood tripods used to be popular because their damping was similar, but quite heavy, not very portable.
Vibration can include several things. Touch it with your finger, or the wind, or the actual camera mirror slapping up open. Delaying a few seconds to settle down first helps several things, but not the wind for example. The sturdier the tripod, the faster it settles down, and the less the wind shakes it. This is seen at higher magnifications, and over longer times of course.
Some of the camera models have mirror lockup, which today works so that the first shutter button opens the mirror, and the next one takes the picture, and closes the mirror. No mirror vibration. Live View mode would be similar, in that mirror opens early.
Some models have few seconds delay after mirror opens and before the shutter, which is about the same thing (except for the timing of the shutter). Not applicable to Live View mode, which already does it.
The camera self timer gives you time to get your finger off of it, and let it settle down. This ought to be used a lot (for those slow shutter or long focal length situations that give jiggle problems).
To have a better idea - Put your camera on the tripod, and select Live View mode, and then magnify the view finder to something like 1:1 size, actual pixels. I am thinking stars at night, but subject could be anything. Then reach up and touch it, as if to focus it. At high magnifications (actual view), it makes focus about impossible, because it is bouncing around too much to see if it is in focus or not. That would not be a stable situation. The same thing happens to your telephoto pictures.