Posterior pelvic tilt

Well, the pelvic tilt in riding is something I have been reading up on and analysing for a while. The Pilates exercises I have been doing call for a neutral spine and vertical pelvis which is great for engaging of abdominal muscles.
However, for riding, the secret apparently lies in posterior pelvic tilt achieved by the use of abdominal muscles (or forward scooping of the seat bones, or 'bringing your belly button towards the spine', or 'growing tall' or whatever else trainers call it) - not the gluteus muscles! . Have a look on here to see a person performing a pelvic tilt.
I have been trying to 'listen' to my body when riding so I can understand what I do or don't on some horses that make them go better (or worse) for their owners.
What I noticed is that I seem to naturally have my pelvis tilted backwards and abdominals engaged (i.e. have posterior tilt) but because I don't really think about it I keep loosing the tilt in crucial moments: just after half-halt and before the halt, in canter to trot transitions, sometimes in walk if I am too relaxed which tends to have adverse effect on the quality of the walk and probably other times but I haven't identified them as yet.
Today I really paid attention to how I sat and got quite impressive results especially in trot to canter and canter to trot transitions.
While teaching in the evening I paid mega attention to this in the rider and her horse also improved. It is not always easy for me to spot a rider loosing the correct tilt (if the degree of the tilt is small) so I am trying to train my eyes all the time. The definite sign of incorrect pelvic position are legs in front of the rider (instead of aligned and underneath the rider) and horse behind the leg. The response of the horse seems to be so far the quickest confirmation of correct/incorrect tilt, especially if the riders wears a massive coat ;). The biggest difference seems to be in the willingness to stretch, soften, chew the bit and offer the back.