It's hard to say, but if you look up key words like: "powder down" "asthma" "respiratory" "allergies" and "cockatiel" you will find a lot of information on how it's not the best pairing. It depends on the severity of the person in question and what their sensitivities are, but they are far dustier than parakeets.
I find my U2s dust in places she never even goes-- it covers my furnace filter and I already have 3 really nice air purifiers running 24/7. U2s are bigger, and misting can reduce it some, but you have also asked about "bird keeper's lung" and powder down birds are also more associated with that than non-powder-down birds.
You will not likely get it from a single cockatiel, but I'm concerned because I know how important allergies are to you and your family. The thing is, sensitive people can get it from a single exposure, so this really depends on extremely specific details that I do not have.
My mom is very allergic to cats. If I touch one and get near her, she starts sneezing and her eyes get red. She does not have asthma. Powder down is SO fine, can be really hard to control if you have someone with allergies and asthma in the same house, because you will not shower or wash clothes when you leave the bird room -- you will bring it with you, as will the HVAC system. At the same time,the impact depends on a person's lungs etc. A healthy person around enough powder down birds can develop respiratory issues, but not all do.
I am not telling you not to get a cockatiel-- but I am telling you that it seriously depends, and if you were concerned about budgies, I'd be more concerned about a cockatiel unless your family has spent a lot of time with powder-down birds and had no issue.