Welcome to the Asana Community Forum!
Everybody that has an email with the same domain as the organization is considered as a user.
They would have to be added with a different email, although then they won‘t have access to a bunch of features (just whatever guests can do)
More info here: Is there a way to turn a Limited Access member into a guest? - #2 by Emily_Roman
Setting up a division might be another option for you? Here is a great post that explains it in detail.