Yes, our entire team staff is present during warm-up/conditoning.
We do have different warm-ups. I am betting most others do also. (A different thread could address the different warm-ups, tactics and specifics during this activity.)
Generally: Warm-up work for the team staff is very important both for the event or core disipline, fundamentals, stretching as well as hearing/seeing/listening to gather tidbits about emotive modes/muscle sore or hurts and matching it to the days workout planner. I use the time to check-in with staff about any issues/set-up/special situations they might see or encounter in the workout.
Our conditoning is scheduled within the workout. At the team conditoning time, according to the schedule, all team groups split into groups and begin their tasks. The tasks are broken by level, or athlete (if on injury recovery). They go to stations/areas manned by staff. We rotate the staff thru all areas. The goals are clear for staff and athletes. Weekly staff meetings we have permanent agenda checks of warm-up and conditioning.
Our gym asks the athletes to present workout and event discipline. Our staff's efforts during warm-up and conditioning should set a model for the event discipline.
Best, SBG -