Uh... no. That shouldn't be happening, certainly not repeatedly.
Yes, fog can trigger asthma!
But you (theoretical haunt owner) should NOT have a worker, especially underage, who you know to be susceptible, in an area with fog. Something's gotta change, either that person needs to be in a different area away from the fog or no fog used. It's dangerous and irresponsible to allow them to continue to have asthma attacks.