I have had the fortune to be taught by one of the top Alexander Technique teachers in the country, who is also a renowned concert pianist. She has spent 40 years looking at piano playing in the light of the philosophy and attitudes of F M Alexander and it provides the most remarkable approach to the piano, developing a deep sense of logic and clarity, freedom and mindfulness.
Technically it is often about what we don't do rather than what we do do. Someone described it as the 'Zen' of piano playing! This is a good description. A piano key weighs about 2oz yet the strain that many pianists place on their whole body just to depress this weight is enormous! All that is needed is a release of energy, from the fingertip, directly down into the key. If a student is sitting straight then no muscles are used in holding the back up as the vertebrae are balanced, and the arms can be supported from the solidity of the back rather than the tension of the biceps or triceps. The body isn't made to sit in any position, but just allowed to find this natural supported posture.
The action of depressing the key is a tiny but precise and sensitive release of energy through just the fingertip. The rest of the hand is loose and unstrained and the finger depressing the key returns to this unstrained group of muscles within a split second of playing the note. It is very similar to switching an electric light switch of the rocker type.
A teacher will have given excercises during a lesson to help develop this. Certainly I do. You should be able to ask as often as you like for demonstrations.
As it is about developing habits, short very focussed bursts at this is better than long protracted sessions with concentration slipping.
Thumbs are a problem for pianists and are where a lot of the tension in technique is created. The impetus for the movement comes right from the tip. None of the muscles should need to be used and if you feel the fleshy pad of muscle at the base of the thumb it should remain squashy during the action. Again, there are excercises for the thumb that will help develop the freedom it needs.