Well, that there could be another reason why they're having trouble trusting you. They just got moved outside, and the entirely new surrounding is startling to them.

You're not allergic to animals, are you? Because the only way for anything like an asthma attack to be triggered, is if you're allergic to them.

You could try explaining to them that since they were born into captivity, they're clean from any of the diseases that are usually found in wild birds.

They're actually more likely to GET diseases if they're outdoors being exposed to wild birds. Taking them out of the cage outdoors is dangerous too. Cockatiels are strong flyers, and if they catch the wind right they can fly away whether they're clipped or not.

Can you get a small air purifier? That helps take the tiel dust out of the air, and the regular dust too.