I am not an advaitin either, but for the sake of argument...even if the fire is considered unreal, there is still no reason to believe that an unreal thing cannot cause reactions. Otherwise, it'd be impossible to explain as to how an unreal dream (because dream, by definition, is unreal) could cause reactions. Nor can we consider the dream to be real, because that would be a contradiction in terms.
So advaita considers such *worldly realities* to be vyavahArika satya-s, which become totally false on waking up, similar to how a dream (which appears totally real, note the word 'appears') becomes false on waking up. Not that I am convinced by this argument, but at least there is some logic to advaita, and it isn't as absurd as most 'pseudo-vaishnava-s' and HKs would have us believe.