Luckily, Psittacosis is not deadly, and is treatable it caught in time, but the main concern is it is zoonotic (can transmit to humans) and make people very ill. It's really your decision whether you want to wait until everyone is treated and tests negative again. Hopefully the breeder will sanitize thoroughly enough in the environment that it will be totally gone.
Now, with whatever practices let the disease in the aviary in the first place, I'd worry what 'else' might be lurking in the aviary. Something more serious like a deadly and contagious viral disease that there are no outward signs of?