"Doing an exercise means nothing, Doing an exercise 100% proper means everything."
The stability ball supine (facing upwards) is the base for many exercises on the stability ball which use resistance.
The key is to be able to become completely stable from this position. If you cannot do so, you MUST regress to corrective stretching, and floor exercises.
Your glutes must remain contracted for this position as they are meant to be the primary muscle for support in this position.
If you hold this position for an extended duration of time, your glutes should fatigue first. If your hamstrings or lower back perform first, it is a sign of muscle imbalance and postural distortion.
San Francisco Personal Trainer Michael Behnken, MS, NASM-CPT-PES, CSCS