Read Dharma Mittra's response:
In my classes, the main focus of the spinal twist is the squeezing of the internal organs. When practiced properly, this flushes the organs of toxins and impurities; pours in fresh, oxygenated blood; and regenerates the entire system. The actual rotation of the spinal vertebrae and the movement of the spinal discs are the secondary focus that supports the deeper, internal benefits.
Twisting should always be done with great attention and care so as to not strain or injure the spinal column. The sacroiliac (SI) joint is one of the largest in the body, and it moves in small degrees of tilting, sliding, and rotating. The foundation for all twists is working with a naturally elongated spinal column. This automatically provides the proper alignment to twist deeply while gaining the maximum benefits of the pose without any stress or strain. When twisting, the idea is to move all the joints in the spine--the lower, middle, and upper, not just the areas where you feel most flexible. Instruct your students to work with the breath, so they can lift the chest and rib cage to twist from a place of expansion instead of compression, creating space around the discs in the spinal column. From this space, they will be able to rotate with comfort and ease, while being mindful not to push too hard within such a limited joint.
In some easy twisting postures, the idea is to keep the pelvis generally stable; but please note that some pelvic movement is not against any rules. Each individual human body has its own restrictions, and a teacher must use discretion. In some advanced spinal twist variations, the pelvis turns as well, as in Marichyasana I and II (Pose Dedicated to the Sage Marichi I and II) and Parivrtta Trikonasana (Revolved Triangle Pose).
If your students experience any discomfort in the lower spine after twisting, it may be that they are simply pushing too hard and compressing the spinal discs. But be mindful that the pain could also be due to something seemingly unrelated, such as different leg lengths or a past injury. Advise your students to stretch out in Balasana (Child Pose) and practice deep relaxation whenever they feel pain before or after postures. If the pain is severe, encourage them to consult a physician.