It depends upon the exercise. Most of the exercises encourage you to keep the heels down but for some of the exercises you are required to bring the heel up. Some of the exercises start with the heels up: for example the exercise #1 Downward Dog where the heels go up naturally. It is important you assume the position as close as possible to how it was demonstrated on the video or manual. Please do review the video to see how the heels position changes as you perform the exercise. It is also vital that the stretch is felt on the right area or muscle to make sure the stretch is effective.
If your heels go up when they were supposed to be down it means you have tight calves or Achilles tendon. Continue with the exercise but make sure to incorporate heel cord stretching exercises.