Ideally, gymnastics and cheer tumbling technique shouldn't vary all that much.
The one notable exception is standing tumbling, especially standing tucks. Gymnasts are taught to keep their center or gravity lower in standing tucks, resulting in them rotating closer to the point of take off. The reason for this is that they are being trained to land accurately on a 4 inch beam. The higher the tuck, the greater the margin of error for the landing.
As for the OP's example - A pike is indeed a logical step in the progression from tuck to layout. A tuck rotates much faster than a layout. This is because bringing the body into a tuck position speeds up the rotation of skill. If you need proof, you can research angular momentum, and rotational inertia, but a much more fun experiment would be to spin in a computer chair, then alternate between tucking your knees, and opening back up. Note the effects of tucking your knees!
Anyways, one of the biggest things I see in kids first starting their layouts is that they throw their head back, or pike down. I believe that this is their instinctual way of trying to rotate, because they are not used to the slower rotation of a layout. I also believe that many times, it is due to a lack of core strength. The amount of strength needed to keep the body straight and rotate is insane, when compared to that needed for a tuck. (try holding a hollow position on the ground with arms up vs. down, and you will see how an increased length of a level can have tremendous effects.)
A pike is the middle ground between the two. It lets you begin to open the body, building strength and awareness in the air. As you become stronger from repetitions of pikes, you will be able to open more and more.
Anyways, that's just my two cents. Enjoy.
-Matt Faherty