I am not a teacher but I have given tuba lessons in my 20-odd years of playing. Here are some thoughts - see what you think.
Posture is most important when playing larger instruments, especially, as I lost a big chip out of my front tooth when the BBb tuba I was playing as a kid swung towards me, off its stand, and smacked me quite hard. I also had some lower back pains in later life that could be attributable. LESSON: Is the instrument the right size for the student and is s/he able to sit comfortably, properly, and safely with it?
Larger instruments take a hell of a lot of filling. Proper breathing, understanding the mechanics, is more important for tuba playing than any other instrument (Please, other brass players, I know its extremely important, too, but even more so for us). My sound, articulation, and intonation developed beyond belief when I read about the subject and followed some tips provided by the late, and great, John Fletcher. LESSON: Correct breathing mechanics equals better playing.
Larger instruments are less likely to be properly maintained, eg. a good bath every so often, properly lubricated, etc.. Its size makes it difficult for the student to do this. LESSON: Check condition of instruments periodically and offer cleaning help.
John Fletcher exercises for more advanced students include: (1) Play scales that exercise the 3rd finger, eg. EEb bass f#, g#, a#, b, c# and down again is a good one, (2) Play scales without use of tongue - develop articulation with diaphragm control, (3) Breathing exercises can be done on way to school without your tuba, (4) Hang outside the school bus by your 3rd finger to make it stronger (true) - but I don't recommend this one for safety reasons.
There are lots more things, of course, but get these basics right and…….