I don't know, I always apply the semi-permanents (SFX, Manic Panic etc) I use on dry hair. I find it's not that easy to apply when my hair's damp and I get a better idea of where the colour has been applied well, when my hair is dry. And at least the semi-permanents I use, don't turn weird colours when I apply to dry hair. On the contrary, when my hair is damp it's more likely that I don't apply enough dye or miss a spot. O_o
Maybe you're supposed to apply to damp hair to get better coverage and because it's supposed to make it easier? I'm just guessing.

But I have heard it too that some people apply dyes on damp hair. But not sure why.