It doesn't say anywhere that they will be non-teaching staff. In fact, in the article, it says this:
The plan would take staff members — including assistant principals, secretaries and counselors — away from their work for middle and high schools and place them in non-teaching roles supervising children in elementary schools.
Note that the interpretation of what it means to be a staff member is Stein's...not wording from the policy. And the adendum says "including" not "limited to". As in, TEACHERS too...who are staff members.
Additionally, later in the article, it says:
Jackson said principals have been asked to select the staff members who will be dispatched to CARE classrooms.
So which is it, principals are picking or it's non-teaching staff? There are only so many secretaries and counselors per school