I saw two Hyundai solid mercury amalgam based helical lamps in the hostel i live that turned on from cold state at full brightness immediately. Is this behavior is normal for an amalgam based fluorescent lamp? Is amalgam based fluorescent lamps turns on at the same initial brightness as the liquid free mercury based fluorescent lamps?
If not, then the israeils advertisements for these Hyundai "Amalgam" lamps appears on their packages (Plastic blister cards slightly similar to the US CFL lamps packages) and also in the site that dedicated to these lamps are lies extremely. (These Hyundai helical "Amalgam lamps" CFLs have an extremely aggressive distribution in Israel because they are appears not only in electricity shops and ACE hardware like stores, but also in supermarkets and even electrical appliances stores. In short terms: Everywere).

Liquid mercury free is in fact an amalgam.
And all amalgam have to heat up somehow, to get the correct mercury pressure - strong bonds to other metals is what make the amalgam behaving as "coldest spot", while it's absolute temperature is way higher. And what is the exact temperature/mercury vapor pressure dependence, so optimum amalgam operating temperature depend strongly on it's composition.
And by it's placement might be influenced, what would be it's operating temperature.

So when the amalgam is placed close to filament (e.g. on it's support) and designed for very high temperature operation (present there), so it heat up quickly (does not have to wait for glass warm-up), but stay on the same temperature (stabilized by radiation cooling), even when the tube itself warm up, so upon few seconds (so practically instantly) after startup, the amalgam temperature is constant, so the mercury pressure.
They might boost the power up for cold lamp to compensate for lower efficacy when cold, so the brightness is full upon start.

Btw: It even came to my mind, then "famous" ALTO's might use this method, but the poor assembly quality (frequent joint failure) made the amalgam pellet to fall off from it's designed place, so then it would not be able to attain required operating temperature, so the mercury vapor pressure in the lamp.

Medved: So also the environment friendlier solid amalgam based CFLs can lit with full light output immediately?

Yes, but if it has to be really immediately, it has it's cost in the lifetime, as it would require power boost for this, what mean higher electrode loading, so wear.

Btw: This method is essential for automotive HID's, where the instant start to specified light flux is required, so ballast has to deliver into 35W rated lamp about 90W upon ignition, as the xenon discharge (used as buffer to have at least something capable to emit light when cold) is very inefficient compare to Na-Sc halides, what evaporate few seconds later (so the power is then reduced to 35W to keep the light flux constant at specified level).