It must be a specific glitch with your lens, so send it back. I always use the central point focus and have taken several thousand shots with the Tamron on the 5DIII and have never encountered the problem you have found.
Thanks. I'll try talking with local service center, but in any case. I'm still trying to understand from the technical point of view - how the lens could cause the central point focusing glitches?
I mean, the AF sensors are in the camera. The lens does not have, as far as I know, anything that responsible for the work of a specific sensor.
Theoretically, it could block optically the central area, but in this case I would see it all on the pictures.
And the AF with a center point is actually working not bad when the refocusing is performed near by - let's say from 3m distance to 5m. It also can refocus from far away to a near object, but not a vice versa.
Basically, it is almost the same behavior for a single center point like it was for all points before the service has updated the lens firmware.