Well, it will work fine on an APS-H camera, but of course the image quality at the edges and corners of the image won't be as good as they are on APS-C, but will be better than you'd get on Full Frame.
What you are doing of course is cropping the image formed by the lens to the size of the sensor. As with all lenses, image quality is best at the center and drops as you move towards the edge. That's because most of the aberrations (astigmatism, coma, chromatic aberration, field curvature and distortion) do not affect the center of the image and increase as you move further from the optical axis. Only spherical aberration affects the center and that's usually pretty well controlled and drops off very fast at smaller apertures.
Tamron designed the lens to have acceptable image sharpness at the edges of the APS-C frame (It's a Di II lens), so anything outside of that is just a bonus!