Good morning, Batman!
First comment (grab a pencil for this). Ready?
Picking up a pencil is pretty easy, right? What were you aware of as you picked up the pencil? Were you concentrating on the arm movement to bring your hand within range of the pencil? Concentrating on grasping the pencil? Getting it into position?
Set the pencil down and pick it up again, this time concentrating on every muscle you use, every movement. Is picking up the pencil still easy, or is it more difficult?
Imagine yourself asking someone to pick up a pencil. How would you react if they asked you about the transfer to a writing position, if the ring finger should be touching the pencil during the transfer or not?
I don't know how you would react, but my reaction would be, "Dude, just pick up the friggin pencil!"
Do you see the correlation here? You are approaching the trumpet more like Aristotle rather than Plato, cleaving the art of trumpet playing into little chunks while your teacher is trying to get you to see more of the whole. Don't feel bad, yours is a common malady.
I spent a good deal of time trying to wrap my mind around Zen pedagogy for the purpose of teaching trumpet. It works to some degree in achieving an "ahha" experience (also known as Satori.)
What your teacher is trying to do is based on the premise that if the sound is right, the chops will follow. Concentrate on the sound when you play, not your chops. All these Aristotelian chunks describe the symptoms of good playing, not the causes.
In case you are wondering about the RAY OF POWER:
"The finicky thing about air is that, yeah, we must learn the mechanics but then forget about them, because under the stress of performance, as tension sets in, our bodies will lie to us, and it will feel like we're moving huge amounts of air, breathing deeply and supporting when in fact, we are not!
For this reason, I rely on some Vulgano Voodoo and the RAY OF POWER. It involves the Root Chakra, which is located directly at the base of the spine, also known as the coccyx. The chakras have their own mystic qualities, I guess. I don't know for sure, but they do seem to be located in parts of the body where bunches of nerves meet. (The Vulgano version is situated half way between the places we do our number one and number two in the restroom.)
In practice and in theory, imagine (and feel) a ray of some sort (red is the most common mystic color associated with the root chakra) shooting down into the ground while playing. For high notes, imagine (and feel) a more intense ray. If we practice this sitting in a chair, we can notice all kinds of muscles come into play, which happen to be the same muscles used to 'support' the air stream. By taking attention off of the mechanics and experiencing the mysterious, magical and not yet patented RAY OF POWER we can avoid some of the tension involved in 'trying hard.'
Nothing mysterious and magical here really, but the RAY OF POWER does permit me to play with a relaxed but working body."
To replace the "lip" in lip flexibility, I like the "magic bubble" concept:
"When we play a note, the air column inside the instrument has defined and mathematically predictable areas of high pressure and no pressure. In physics these are known as nodes and anti-nodes. The higher the tone, the more of these nodes inside the instrument. With a horn of sufficient light weight, we can play a long tone we can gently run a finger around the leadpipe and/or bell and feel some of the vibrations. Change to a different harmonic and that place will move.
Now for the esoteric part. Playing a long tone, we can shift our awareness to inside the trumpet, and imagine/feel a point of resistance somewhere inside the horn. I call these 'magic bubbles.' To slur up, we can "blow" this magic bubble further away, backing off will allow the magic bubble to return to its place closer to the mouthpiece.
Our body will memorize the feel of these notes and nodes much more quickly than the cognitive control of several variables can. Remember that the embouchure is (or should be, in the Zen Vulgano philosophy)formed in part by the note that it is playing."
One last observation. Nan-in, a Japanese master during the Meiji era (1868-1912), received a university professor who came to inquire about Zen. Nan-in served tea. He poured his visitor's cup full, and then kept on pouring. The professor watched the overflow until he no longer could restrain himself. "It is overfull. No more will go in!" "Like this cup," Nan-in said, "you are full of your own opinions and speculations. How can I show you Zen unless you first empty your cup?"