When I am gardening and move from a deep squat to standing, I get a little lightheaded. It is not really disconcerting, but when it happens when I'm doing Pilates, well that is a different story. Exercises where you move from horizontal to vertical quickly can create a sudden lowering of blood pressure, which can make you dizzy. The most simple way to avoid the head rush is to move more slowly. And moving more slowly will emphasize the element of control central to the Pilates philosophy. This will also increase the difficulty of the move. Think of that as a perk brought to you by your desire to avoid a head rush.
The expert at About.com: Pilates also thinks that increasing the "scoop" of the deep abs on the inhale can help keep the blood pressure from dipping too low. Keeping the low and deep abs engaged while you breathe in means you need to focus on breathing into the sides and backs of your ribs — an element of Pilates we can all work on.
Try these two fixes and see if they keep getting dizzy at bay.