Hey Angi,
When I first started diving I was diagnosed with asthma, I think it was 30 years since I had used an inhaler. I never had an attack while diving, I think it may have to do with the dry compressed air. I know I am an unusually calm diver but I remember not telling my dive instructor 30 years ago that I had asthma in fears that he would not certify me, but keep in mind I was already diving since 10 years old with my uncle.
When and if your student gets past the ok from Dr I will help out with them at the springs with you, and I can stay with them the entire time, the also need to have a very warm wetsuit, that cold water shock can trigger an attack.
To put your mind at ease we have dove with some people with asthma just recently, as well as major heart issues as well. He was sucking on an inhaler just before his roll off.
I also think it has a lot to do with severity of their condition as well. The doctor may also recommend they use nitrox, which is the case of the fellow we had dove with.
Good luck to you and them, Just think it could be a good learning experience as well as something you may even choose to specialize in. Sometimes the greater the challenge is the great the reward is for your soul.