I have no first hand knowledge of the transfer process so this response is a best guess based on sending 4 kids to college.
I assume he applied and was accepted at the designated school. You will want to watch the calendar and comply with their process of acceptance (fees, housing, etc) as you wait out the transfer process. Depending on the calendar, you may have to start sending in deposits before you get your final NROTC outcome. You may get a refund but often they are non-refundable. Still better to lock in a spot than lose it.
Same with Norwich. If he was accepted and would go there without a scholarship, then you want to stay on top of their admission process. He could always go there and reapply next year or take an alternate commissioning path.
Since your DS did not get Norwich right out of the gate, that means there were already filled up. Your son is on the wait list and if someone drops, they will work the list. I suppose he could call the Norwich NROTC detachment but not sure they have visibility to the list (or would even tell him). Perhaps someone who has first-hand knowledge of this can give you better insight.