The mention that TV cameras are Parfocal is really key: https://en.wikipedia.org/wiki/Parfocal_lens
Which means that you can zoom with it without having to refocus, which is not the case with less expensive lenses.
Which means that you can zoom with it without having to refocus, which is not the case with less expensive lenses.
It's not perfect — there's always a lag of about 6 frames during fast zooms — but it's "good enough" for most situations (which means it's not ready for broadcast).
One thing to keep in mind though is in big production sets they are not using automatic focus at all, and cinematic lenses don’t tend to have focusing motors. (Also a focusing motor for a 100lb lens would likely be very noisy).
Older box lenses use a convoluted set of gears to achieve the same thing.
Some handheld ENG lenses for shoulder carried cameras get close to parfocal by making the lens elements travel in a complex way, but its not as perfect as the box lenses get.
The zoom position and focus position is worked out by moving the front and back elements of the lens, with a bit of adjustment so they track together properly. I actually have a nice old Sony V1E where the back positioner has failed (or become disconnected, possibly) so it never really looks right, and it would be too expensive to repair. It works great as a DV playback deck, which seems like a bit of a waste I guess, but repairing it would be about the same price as buying a working one.