Question in the title.

Never heard of those.

I would suppose it warms up quickly because of the different materials, And small size.

According to the video it is by far not few seconds, but about a minute or even a bit longer. And that is pretty normal for the ball shaped CMH's and even HPS, mainly of such low power rating.
It does saturate the camera within few seconds, but that is by far not the full power at all. You have to look how the camera readjusts the exposure time, so how the background darkens and mainly how the color changes. Cameras do that within few seconds, so the camera readjustments follow the lamp with just a few second delay. And even with that in account, there you can see it is definitely longer than a minute till it really settles.

The only lamps ive know to warm up that quickly are the automotive 35w "xenon" MH lamps. Most CMH I would say around a minute to fully achieve stable color and intensity.

The automotive MH lamps runs-up in seconds because that their ballasts boosts their current during run-up. operating them on a regular 35W MH ballast, will result in slower run-up and lower initial light output.
Someone here said that the Cosmopolis runs-up much faster than the regular CMH lamp.

What makes  quite a lot of difference is the ball (the new CMH's, the Cosmopolis belong to these) vs cylindrical (the "classic" design) burner shape. The ball is indeed way faster than the cylinder, but that means about 1..2 minute range needed for the "balls" compare to 2..4 minutes for the "cylinders" of equivalent wattage and ballast. In fact this is one of the aspects, why the ball shape offers longer life: The time, when there is plenty of molten, but still liquid halide pond dissolving the arctube becomes reduced (the halides evaporate quicker), hence the slower progression of the arctube degradation.

It is true, the electronic ballasts do feed the lamps at higher power for the runup, so then the runup is faster than with magnetic, but these have to stay within the bulb specification (if I remember well, a rectangular current may be up to 2x the nominal arc current; the magnetic exposes the lamp to that during peaks and only for a short time after ignition, the electronic is able to maintain this current so long, till the arc voltage does not indicate the lamp becomes nearly warmed up or till the resulting power does not reach the set power limit on the simpler ballasts). Again the reason for this is first the convenience of faster startup, but mainly shortening the time, when an abundance of liquid salts may attack the arc tube.

What order of run up overload would be ok for Magnetic ballast for small lamps ? (20..70 W)

What order of run up overload would be ok for Magnetic ballast for small lamps ? (20..70 W)

Normally the magnetic load the arctube by a current with peak value about twice as high as the rated normal operation rms current. And that is, what the cathodes of the lamps rated for magnetic ballasts are designed for for the startup.
So for the 70W with 1A nominal arc current it means 2A peak during runup, the 35W lamp (0.5Arms) means 1A peak and so on.
As far as I know, the 20W lamps are rated only for a ballast with active burner temperature control, so are rated only for an electronic ballast. But if I remember well, I have somewhere noticed the startup current rating around the 0.45A, so that means their design follows the same rules.

For the magnetic ballast current you have to be careful: What counts is the peak value, while the magnetic tend to slightly saturate when the arc voltage is low (early in warmup phase), so that means quite little margin (so no more than about 20..30% above the burning rms current rating). And as the arc voltage rises, the current goes down. That is, why the magnetic ballasts ca not utilize the cathode robustness for faster runup. Or better to say, the fact the ballast characteristic imposes a need for the cathodes to handle the peak current corresponding to double the rms rating allows the electronic ballasts driving the lamps with lower crest factor and with current capability independent on the arc voltage to utilize this difference to boost the average lamp current, so boost the power delivered to the lamp during startup.

So with magnetic ballasts you can not go faster, as these already use the complete lamp rating for the startup peak current.

I can avoid the saturation problems if instead of 1 ballast i wire 4 in 2x2 series/parallel. How far can i go then ?

As already written" Peak value is limited to 2x the rated rms arc current, there is nothing fancier. That means if you maintain the sinewave, the rms current for the warmup may be 1.4x the rating.
But of course, the current (so mainly the delivered power) should be reduced back to the rating before the lamp overheats.

Here I'm not sure, whether the speedup by just 40% extra current is really worth the complexity, but that is up to you to judge...

My portable Xenon lights warm quickly-essentually "car" headlights in a portable form with a rechargeable battery.Another quick heat HID lamp is Xenon projection lamps-as close as your nearest movie theater.Yes,digital projectors use the xenon bulbs-to be replaced with RGB laser illumination in the future.Also the quick heat of car type HID lights is the very small high pressure arc tube and just the xenon adn the halide salts.The arc tubes in these lights are smaller than the full size line voltage powered HID lights.

What makes  quite a lot of difference is the ball (the new CMH's, the Cosmopolis belong to these) vs cylindrical (the "classic" design) burner shape.

OK, that explains why my recently acquired Philips CDM 50W (made in 2014) has a warmup time of about one minute, considerably shorter than what I'm used to. I always wondered why they switched it ; now I know (one of the reasons).

Thought of another quick heat HID lamp-the high pressure mercury lamps used in Sony Digital 4K cinema projectors.Depending on screen size and throw distance-the projector uses 4 or 6 330W or 450W mercury High pressure lamps.The lamps are similar in appearence to what was in older RP TV sets.Watched "Batman vs Superman" in a cinema with the Sony projector-very impressive!A good safety advantage of the Sony lamps is the projectionist doesn't have to wear the jacket,face sheild like what would be needed for replacement of Xenon lamps.