How does the Sorcerer flare card work with non-viable races in Cosmic Encounter?
The change is permanent. (Yes, it is powerful, but Wild flares are often powerful; frequently more powerful than the Super, which is usually just an enhancement to the base power.)

The fact that the change is permanent also helps to clarify your question. The defender isn't using the attacker's power; the defender is using their own power, which happens to be the power the attacker started the challenge with. Since it's their own power, its usage is controlled by the number of their home bases.