Hi - I am sure one of the incan guys will chime in to correct part of this, but here is a starting point.
When cold, the filament has a very low resistance, so there is quite a current surge that happens during that first "instant" of on time. This surge can be higher than the battery can safely supply, so the protection circuit goes into overload protection mode. Enough current has gone through the filament to start warming the filament up and raising the resistance.
The protection circuit on the cells can "reset" in some cases, allowing another attempt at starting up the filament. If the filament stays hot enough, and the cell protection circuit reset is fast enough, then after a few clicks (on / reset cycles), the filament is hot enough to have the needed resistance to run with the available power.
That same surge is responsible for a lot of filament damage, so incan controllers often include a "soft start" mode to reduce this effect. If you can, always try to use one of these controllers as it will make your overall experience with incans so much better. Search for threads by AlanB for more info.
As far as damaging the cells - I don't think it does, but anytime you are using a "protection" circuit as your "regulation" circuit, it is dicey.