I will try and get you started here, and then we can get more specific if any of this leads to somewhere you wanna go.
Generally, when you play, both hands/arm and both feet/legs are moving, so the core of your balance and propulsion tends to come from the pelvic, ab, and low back musculature.
My guess would be that your drummer sits at the set with a posteriorly tilted pelvis- I do it all the time, and I know better. Just thinking here, but I would guess the hip flexors/psoas are tight due to lifting the leg while playing.
Lower leg: probably the anterior tibialis needs attention due to a LOT of dorsiflexion. Course the posterior leg muscles could be tight depending on playing style here (a tighter or heavier sound vs. a freer or looser sound i.e. playing
into the drum vs. playing
off the drum).
Low back: See the above part about post. pelvic tilt.
Upper back/chest: Typical for anyone who works with arms/hands in front of them. This would especially be so if his/her drums are not very ergonomic. A lot of players will position equipment where they end up having to reach to hit a cymbal. The ideal is to have everything close enough so that you can minimize any reaching or extraneous movement.
Arms and Hands: How is his/her grip on the sticks? How do they hit the drum? Some folks will play in a postition that puts the wrists into ulnar deviation when they hit the drum, which creates a different impact translation into the wrist and arm then if you hit the drum with your wrist in flexion. Think about knocking on a door vs. a karate chop.
Thier grip will have a lot of consequences, as well. Gripping the stick loosley will allow the impact vibration to stay more within the stick. A tight grip (along with the extra strain on the hand and FA mm.) will move the impact vibration more into the hand and arm. This is especially important if they are playing hard.
Also, in playing a traditional grip, as a lot of jazz players do, will involve more finger movement. Matched grip will usually involve more wrist movement.
Hmm. What else? The FAs can really get stiff if they are not warmed up or stretched regularly. Right hip can be tight from a lot of bass drum work. RSI in the wrist can be common.
That is all I can come up with at the moment, but hopefully that will get you started.
t006