Selecting a house qualifies it with a few exceptions. One of the exceptions is Greyjoy which lights solid because when you’re playing other houses, Greyjoy is running at the same time (it makes all modes harder). Search game of thrones ruleset on tilt forums - it will give you all the detail needed.

Targaryen's power is to start with the house *fully completed* - meaning solidly lit, you don't have to (and can't) start and play the mode. (Thematically, this is because the mode is fighting the dragons, but Targaryen doesn't have to do that, she owns the dragons.)

Greyjoy behaves the same way, playing as them starts with the house fully completed.

The other 5 houses all start with their house flashing but not completed, so you can start it immediately upon your first center ramp shot if you choose to.