Mmmmm ....
...... My advice (I'm sure others have different techniques) ... If you are having trouble with RPM control, go up to 3000+ feet, enter an auto and just play around with the RPM, see what effect cyclic inputs/attitude has on autos, do some turns, get comfortable holding the 60kt attitude and managing the RPM etc. It's a lot easier than trying to learn this while heading for the ground at 500 feet .....
This is exactly what your instructor should be doing .... as well as teaching the effects of varying speeds in the 'auto' to achieve different glide angles/distances travelled etc ....
One of the disadvantages of having a relatively inexperienced instructor is that perhaps he does not know what he should be teaching ?
I wonder how just how well the Chief CFI is supervising his schools syllabus if this is going on?