Broadly speaking when riding English your stirrups are used
Mostly to keep the feet still - as against with Western where they are used to support part of the weight of the rider. Partly the heel is kept down and the toe up so as to help avoid losing the stirrup iron.
The idea of keeping the foot parallel with the body of the horse is to roll the thigh muscle, and to a lesser extent the calf muscle, round to the correct position against the horse.
As your skills and muscles develop the thigh muscle becomes more and more important when giving the horse an aid -eg just a squeeze will instruct the horse to move on.
English riding is all about the muscles in the area of the pelvis - which is why Pilates exercises are so useful.
Your instructor should be able to place your leg in the correct position around the saddle and in the stirrups, which then you will have to learn to adopt at all times
It all comes good with practice but it is very important that you start from the correct position of the leg in the stirrup
With you sitting upright on the three seat bones - hence the need for the instructor - you can't see from where you are sitting if your leg position is correct or if your leg moves when you are trotting.
If you are having difficulty keeping the heels down ie that you have to force them down, then first check the length of your stirrups leathers maybe they are too long?
Also perhaps your hamstring or calf muscles may need lossening up - again do Pilates stretching exercies
Getting the leg and seat position right is the key to the sitting trot.