http://www.youtube.com/watch?v=TmCLQIhU3PI
Is this a normal behavior of an amalgam based fluorescent lamp???
This serious question is particularly for you, Medved.

Only thing visible on the video was an instant start ballast. It does not tell anything, if it was at full brightness immediately, or it gain it with delay. When switching ON any lamp, it look very bright for first instant, as both your eye as well as the camera are set to low lighting levels, so are blinded when it suddenly turn ON.

But i guess you wanted to say, then the lamp has majority of it's brightess just upon start.
At first place would be the use of such amalgam composition, that yield at least some usable mercury pressure at cold. "Amalgam" stay for any mercury-metal compound and it is the exact amalgam composition, what define the mercury pressure as function of the temperature.
Second the amalgam might be placed on such place, where it warm up very quickly: On electrode support wires.
And there is yet another way to get full lumens from lamp not yet warmed up: Overdrive it. By forcing more then normal power you get lumens out even if the lamp is not yet efficient due to e.g. too low temperature. This has two fold effect: Lamp's lumens are "instantly" high and as second, due to large power feed to the lamp, it warm up quicker. The power is sometimes even doubled, forcing easily 40W into 20W nominal lamp.
When the lamp warm up, the power is reduced back to normal. This could be implemented even in seemingly basic ballast design, only taking right temperature coefficient components (ferrite for the feedback transformer, some PTC's in the feedback network,...)
In real life, if such quick lumen run-up is required, all above might be combined together, there are plenty of known and way more not yet known configurations, so no wonder there are lamps able to give full lumens just upon start.
And as nothing is for free, i guess such lamps would have poorer efficacy (amalgam composition) and shorter life (overdrive) then normal lamp without such features.

I think way better example of such system is an automotive headlight HID system. Technically the lamp is 35W metal halide (mostly of Na-Sc) with xenon used as a buffer starting gas. The use of xenon instead of ordinary argon has it's reason: Technical requirements for headlight ask for the lamp reaching it's rated lumens instantly upon ignition (up to 2 seconds after control switch turn ON). As the lamp is cold, there is only xenon to provide any light (Hg is liquid, Na/Sc halides solid), but it's efficacy is about 2..3times lower then the arc in metal halides after warmup. So what is implemented: Lamp is powered by 70..90W just after ignition, while it's temperature is simulated inside the ballast. And as mercury and later halides evaporate, lamp efficacy increases. As the ballast keep track of the temperature, it gradually reduce the power to the lamp, so the lumen flux is kept constant. You only observe this happening, as the lamp changes it's color (Xe -> Hg -> Na-Sc) within the first half minute after power ON, as obviously the ballast can not influence the color composition. And interesting to note, such 35W automotive MH replace only 60..75W halogen, while for general lighting the 35W CMH replace 100..150W halogen lamp with the life about 10khours instead of 1000hours of an auto HID.

Medved: This Hyundai amalgam lamp life was rated 8000 hours as seen in its package. 2000 hour more life than "normal" instant start CFL lamps.
To me its look like 100% brightness upon cold start.
This lamp is 20W, have 827 color, have 1160 lm, its current is 135 mA and its efficiency is 58 lm/w.

8000 hour is the typical life of better quality instant start CFL (and normal 15khour rated fluorescent on instant start ballast} for standardized 2h45min ON / 15min OFF cycle.
(programmed start CFL's are rated >10000h, while regular fluorescents on programmed HF ballast are >20khour)

"look like 100% brightness" might be anything between ~70..100%, when looking at single lamp without direct comparison you can not tell it more accurately. For better accuracy you would have to have two equal lamps beside each other with equal background, one turn ON first and let stabilize, then turn ON the second and during it's runup compare differences.
Or using faster luxmeter.

The "20W" rating mean the power input in the stabilized state is 20W, it tells nothing about the power input in the run-up phase, so it might be double for first few minutes.
And the "135mA" is there as base for calculation of wiring and fusing dimensioning (for large installation). There is allowed temporary overcurrent (above the 135mA) during short time run-up, so again it might be double for a minute.

So, is this Hyundai amalgam 20W lamp will last its 8000 rated life if it is overdriven at cold start?

So, is this Hyundai amalgam 20W lamp will last its 8000 rated life if it is overdriven at cold start?

If it is well made and not overheating during use (at normal power), yes. Depend on tube quality - e.g. impurities in the emitter coat and gas fill tend to shorten the life...

Is there another mothed to get the majority of the brightnes of the amalgam fluorescent lamps instantly after cold state without overdriving the lamp? Because 8000 hours is seems too long to me for an amalgam lamp that overdrives itself to do this.
I asks this, because recently at www.galleryoflights.org "lite-lover" uploaded a picture of his american PAR30 amalgam CFL lamp that made in China and he wrote also that it uses "instant on amalgam technology" like my Hyundai amalgam helical CFL lamp have, and his lamp also have an 8000 hours rated life like my lamp.

The short overdrive does not wear anything as significantly. Don't forget, then it happen only when all is cold. The main stress related to overdrive of a lamp is overheating due to heat buildup, but this need some time. When things heat up, the power already drop to the nominal.
Way more damaging is the lamp cold electrode start. It is the main cause, then the lamp has average life of only 8khours on "standard" 165/15min working cycle.