Kitbag,
A VC10K tanker can fly with just the 4 flight deck crew plus one passenger on the jump seat. This is the standard configuration for AAR sorties from a main operating base. A handful of type-qualified aircrew may occupy seats in the cabin without a Cabin Supervisor.
However, once there are passengers (even just one) in the cabin there must be a qualified Cabin Supervisor to conduct the safety drills. The CS may be an ALM (all qualified) or an Air Steward (not all qualified). If the aircraft is landing away from a main operating base some groundcrew will be carried. Groundcrew are not qualified to conduct any of the cabin drills and must be looked after by a CS. Hence on trail, even in the pure tanker role, a CS will always be part of the crew.
Unlike the VC10K, the C1K requires a proper trim sheet that can only be done by an ALM. The ALM can dispatch the aircraft as described earlier, but clearly this practice can only be employed when operating sorties to/from a main base. Even on a trail, in the purely AAR role, a C1K will probably also have a couple of extra Air Stewards on board. This is so that the correct crew complement is in place to allow the aircraft to be re-tasked into the pax carrying role whilst away. As with airlines, the number of cabin crew is driven by the safety drills and the trolley-dollying is a convinient secondary role.
No mark of TriStar flies in any role without an ALM, and for the reasons outlined above, a trail crew will have Air Stewards to allow for increased pax numbers if required.
I have no idea how the Nimrod and E-3 conduct safety drills whilst carrying their own groundcrew/passengers. Maybe the number of type-qualified aircrew in the back is deemed sufficient to supervise the evacuation of unqualified personnel. Perhaps some of these rear-crew are allocated to specifically supervise the pax in th event of an evacuation?
As an aside, the Air Stewards on the Canadian Airbus are chosen from volunteers from all trades/services. They reason that very little of the ground catering trade training is directly applicable to the job, so why not accept volunteers from any trade for a flying tour. I think this is a great idea and employing some Army/Navy cabin crew would break down some of the "us and them" perceptions. I also think it is much more preferable to have all-volunteer crew, whatever their background