Usually those tests do now show TOS, they are mostly done to rule out other diseases. It is diagnosed by physical examination.

You can see a video here, it explains how it is diagnosed.

http://www.medscape.com/viewarticle/748666

I am not familiar with PT for scoliosis but there is specific physical therapy for TOS.

Those include nerve glides, manipulation of the first rib if it is elevated, neck stretching ( this is controversial because some people get worse with this, it has worked well for me). If you have bad posture your upper spine is probably quite immobile and the physical therapist will manipulate those joints as well. I also go to chiro twice a week for that.