It isnt that they have multi-color dyes, its that certain dyes have wildly different colors depending on the specular map of the material it is applied to.
Transliminal Violet is perhaps the most outrageous of them, but many of the rare or unusual dyes have this property to a greater or lesser degree.
Entoloma Blue (crafting a legendary item and applying a legendary enchantment you also created to it) is a lovely turqoise/teal that is a rich dark brown on any matte surface (no or almost no specular) and aforementioned turquoise on any shiny surface. Metal its just straight blueish, but on leather is where you get highlights of the color, and the brown on the matte sections.
Lamaes White (from reaching rank 10 in the Vampire skill line) is a great bright white, but it flashes a light blueish/opalescent with high specularity materials (though it is just a bright silvery white on metal)
The best way is to just experiment and try the dyes on many different types of material to see how it responds to the different specular maps on different pieces of armor. Knowing the changes are based on the specular, you can make educated guesses on what bits will take the dye best.
The leather elements of the Ebony Light robe/chest is a good, very noticeable piece of armor to test dyes on, as the specular on the raise decorative elements is incredibly high, while the base surface has almost zero specular, so you get a really sharp, clear image of the range the color can go without too much experimenting, though you have to keep in mind the effect wont be as crisp and cool looking as on the Ebony leather elements.
TL;DR
Experiment, try dyes on different types of materials to see what they can do!