Yes, I would make efforts to try to determine if a stay put policy is actually safe in the building (by examining the compartmentation and smoke stopping facilities in and above corridors, etc).
If stay put is not viable (due to insufficient compartmentation or smoke stopping capabilities) then some evacuation strategy should be devised based on the aim of getting people at risk to a safe part of the building with the ability to continue their escape if necessary - it all depends on the layout. In this case, the staff will have a significant role to play in the evacuation.
If stay put is viable then I would recommend that the fire alarm system be adapted. Each flat/flatlet should, of course, have its own sounder facility for the occurence of fire within it (i.e. part 6 or equivalent) - the part 1 system may be able to be programmed to facilitate this. But there is no reason for a general raising of the alarm throughout the building, there should just be some mechanism for alerting the warden in the case of fire detected anywhere in the building. Pagers, or similar, linked to the alarm panel can work to alert the warden or maybe (to save costs) a low level general intermittent alarm that the warden can hear anywhere in the building. This should remove any confusion that might currently exist. In this case, there will be only a very limited evacuation but the staff should be involved in this. There are probably some common rooms to consider and careful thought will be required to determine what parts of the building should be evacuated in the event of fire in these areas. Again, it all depends on the layout.
Of course, the current system will work, but it is confusing and can lead to a tendency for people to ignore the alarm sounders. It is also disruptive and inconvenient. Whatever system and procedure is chosen it should be as simple as possible.
Stu