Vignetting: RAW vs jpg
If you open a RAW file of a shot taken with the Tokina 14-22 mm f/2 in Photoshop or Lightroom, then you will not see any vignetting. Across the whole zoom range, the vignetting in RAW files is about half a stop. If you use a smaller aperture, the vignetting is even more limited. RAW files that are opened outside Lightroom or Photoshop also show no visible vignetting. That is a very good performance for a wide-angle zoom lens.
If you store pictures in the camera in RAW and jpg formats simultaneously, it can be that you see a striking difference between the RAW and jpg file of the same shot:
Tokina AT-X PRO SD 14-20 mm f/2 (IF) DX:
RAW files even at f/2 almost without vignetting
That does not come from the lens, but from the image editing. The amount of vignetting in jpg files depends on the image editing that is applied by the camera. In the Tokina 14-20mm f/2 review @ Lenstip , jpg files from the Canon 50D show vignetting of nearly 1 stop and a half stop is only reached after stopping down two stops (f/4). If you save a picture in a Canon 760D simultaneously as a RAW and a jpg file, then the jpg file shows one and a half stops of vignetting at f/2. JPG files that are stored in the Canon 760D even still show 0.75 stops of vignetting at f/5.6.
Lenscorrections in Lightroom: RAW files only
Ever-more photographers apply automatic lens corrections in Photoshop or Lightroom for vignetting, distortion and chromatic aberration. That can be done batch-wise by applying the correction in 1 shot, and then selecting all the other shots that are made with the same lens and synchronizing the settings of these shots. This is a good reason to shoot in RAW, because in Lightroom and Photoshop are almost no lens correction profiles jpg available.
That the RAW shot shows so much less vignetting than the jpg version is not caused by a lens correction that is done by Photoshop or Lightroom. If you were to apply a lens correction, then the vignetting of the Tokina 14-20 mm f/2 would be even less.
At the time of this writing, there is not yet a lens correction profile available in Lightroom or Photoshop for the Tokina 14-20 mm f/2. As a temporary solution, you could use the lens profile of the Tokina 11-20 mm f/2.8. After correction, the vignetting is completely invisible, as you can see the example below, where a Canon 760D jpg shot is compared with a corrected RAW file from the same camera, made at 14 mm f/2.
Moreover, not everyone wants to correct for vignetting. In some portraits the edges are darkened using the vignetting correction tool in Lightroom or Photoshop, so that the subject seems more illuminated. Photographers using a camera with a full-frame sensor, are - usually without knowing it - used to 1 to 2 stops vignetting.