Farmed salmon are not dyed to attain their characteristic orange/red colour.

Farmed salmon obtain their characteristic colour in the same way the wild salmon do - through vital carotenoid nutrients in their feed called astaxanthin and canthaxanthin.  Salmon require these essential nutrients for health and reproduction.  Like many carotenoids, these nutrients contain a reddish pigment that is retained in the flesh of most salmon.  Wild salmon obtain these carotenoids in their diet through small algae-eating crustaceans, while farmed salmon obtain them through their inclusion in their feed.  The carotenoids added to the diet of farmed salmon may be from natural sources, or may be bio-identically synthesized in much the same way as Vitamin C is synthesized for inclusion in human diets.