This is my understanding of how the CVT operates in the situation you mentioned:
If you are stationary in 'D' with your foot on the brake the gearbox puts itself into neutral (even though the lever is in 'D'). When you take your foot off the brake it engages Drive, and then you can pull away. On my CVT I could just about detect the engagement. Perhaps you are getting onto the throttle very quickly before drive is fully engaged, try taking your foot off the brake without applying any throttle and see what happens. In the 'S' position it doesn't go into neutral, drive is continuously engaged ready for a quick getaway.