The APS-H sensor has a crop factor of 1.3X, rather than the 1.6X of the (Canon) APS-C sensor. Third party APS-C only lenses are designed to work with 1.5X crop sensors and smaller, which essentially means that their image circle will be large enough for any APS-C sensor with a 1.5X crop or larger crop factor.
This means that these lenses won't work with APS-H sensors, they will vignette very heavily.
However, when zooming in with zoom lenses, the image circle grows much bigger. This means that these lenses designed for APS-C, will, from a certain FL onwards, no longer vignette. The same is true for the use of these lenses on FF too, BTW.
The cut-off point for the disappearance of this vignetting varies a lot with the design and FL of these lenses. With the Tokina 11-16, I think it will no longer vignette on APS-H from around 13 mm, and from about 16 mm for FF.
The Sigma 30 is a problem, because it is a prime, not a zoomlens, and will therefore vignette on APS-H full-stop. What you might find, though, is that when focusing up close, it may no longer vignette, or not as badly, because the image circle also grows bigger when focusing closer. I couldn't tell you off hand at which distance it would be vignetting free, however. Magnification wise, it probably is at around 0.25X, which likely is going to be at MFD or close to it. Its usefulness on APS-H will therefore be limited, if usable at all, and you may want to consider replacing it with a FF 28 to 35 mm lens as a result, to retain the same approximate FL on both bodies. Canon has the 28 F/1.8, 28 F/2.8, 35 F/2, 35L, you could maybe even consider the 24L or 24LII, and Sigma has a 28 F/1.8, and a 24 F/1.8 too if I am not mistaken.
Do note that 3rd party APS-C lenses, as they are designed to work with cameras with larger flange distances than Canon bodies, and because they use a standard EF-mount, will mount and work with the larger sensor Canon cameras without a problem, except for the vignetting of course.
HTH, kind regards, Wim