As to your question about if that is normal consider the shape of a cow horn. Buffalo horn is similar in shape. Now it is cut then spread out and pressed flat.
I have never used a steam heater but I don't see why you couldn't. You can also immerse them in hot water then clamp them between 2 pieces of wood but make sure to dry them off first. Whatever you do to heat them you will need to clamp them while they are still hot and pliable. Especially if you use water to heat them with be prepared to leave them for a couple of days.
You are going to have to shape them though so you may want to do that first. You may not have to flatten them as much once they have been thinned down. Horn has a kind of memory for shape sometimes they will tend to revert to the warped shape. I am working with a pair now that I have flattened repeatedly and they keep warping back some. Sometimes you may have to flatten them several times.