Well, then your trainer is not giving you particularly accurate information. Rolls and thigh blocks help with a loose leg or tired or somewhat unfit rider ( as in typical Adult, self included. They do nothing, nada, zip to keep you in position over any fence and those who ride the big sticks will tell you these things get in their way as they try to melt into a horse giving big jumping efforts.
Besides the fit issues, the truely supportive saddles have a definate " sweet spot" where the seat puts you in perfect position and allows your body to keep you there. Best one I ever rode in was an Hermès. Looked flat as a pancake, sat me deeper and closer to the horse then anything else ever did, Oddly more comfortable then the cushier saddles. It was probably 25 years old at the time, still in use today.
Look for used, better name saddles. Me, liked that Hermes but preferred my Butet and Childric for my aging carcass and 3’ Hunters. As this trainer might if she’s older and riding a lot of horses. But I sure would never claim the cushier saddles kept me more secure or even on the horse. Just softer on me and had no need for a 4’+ saddle.
Obviohsly, you need something different for CC but it’s that sweet spot you want to feel, not rolls and blocks.