I don't understand what that particular Tamron lens brings to the table vs the Canon EF 35mm f2 i.s.? Yes, the Tamron is f1.8, but 1.8 vs f2 for all of the complications?
At least speaking for the Tamron 45mm f/1.8 (and probably also for its very similar 35mm cousin), it seems to have better image quality (bokeh, CA, sharpness), weather sealing, metal construction, an extra stop of image stabilization, and going for about $100 less on the used market for a good copy. The Tamron lens also has a significantly closer minimum focus distance. I haven't encountered any problems with it in my Canon EOS Elan 7E (made in 2000). I can get sharp shots with it at 1/6 half the time, or 1/10 reliably.
I also have the Canon EF 28mm f/2.8 IS, and I can handhold it at about the same speed as the 45mm Tamron. You would expect a little more since it is wider, but the stabilization isn't quite as good.
For the Tamron 85mm f/1.8, 1/15 is the slowest speed I like to handhold it.
For film, the Tamron 35mm through 85mm f/1.8 lenses all need a stop-down to f/2.8 to eliminate the vignetting. Though the 85mm is fine vignette-wise at f/2 for medium or high contrast subjects and that is the aperture I use most for portraits with it, which usually are good with a little vignette.
It's great, especially in harsh-weather climates, to be able to slap a UV filter on the Tamrons, use them with their hoods and not worry about rain or snow. My camera is not even rated as weather sealed but the combination hasn't let me down, must have shot it in bad weather a dozen times this winter.