Alternate usage:
What if you wanted to perform a spell that removes the fire from all of the burning minions (and maybe the scene, as well) and turns it all into a huge fireball to hit the big bad? It could be argued that because the spell is meant to make magical "contact" with all the burning minions, that all of those minions' "On Fire" aspects can be tagged. Would this be something to allow?
I think this is Fate Point territory. It's not making magical contact with the minions so much as establishing Aspects which can be used.
Visually, I see what you are doing, but ultimately, rather than granting a +20 to the roll to remove those Aspects from the mooks and use them to hit the Big Bad, I would count it as a serious Compel against the Big Bad, and charge 2+ Fate Points depending on how much narrative grease is required to make the Big Bad go away.