Hi Martin,
This is an informal investigation time allowance (two stages, in effect). This procedure does tend to get adopted (informally) in premises that have a single stage alarm but that are troubled by false signals. They have probably found that virtually all alarm actuations are false alarms and so have adopted this pragmatic but not fully safe procedure to meet their needs. They don't normally want any evacuation to start on first actuation of the alarm but only want the staff to investigate. If a fire is confirmed, their procedure will be to re-sound the alarm and the continuing warning signal will inform staff to commence evacuation. That's the usual scenario and yours sounds like it fits in with this.
There are a number of potential problems with this, some possible ones are:
No structured investigation procedure
No contingency plans for unstaffed security hut or where investigating person becomes incapacitated by fire
No definite time period for the investigation time, after which evacuation commences
No double knock recognition
Potential confusion among those hearing the alarm (as you stated)
Somewhat complex procedure which increases chances of human error
These are just some problems that come straight to mind, there are others.
I don't quite understand the "start/stop button." Is it a very old panel? And/or a very simple system?
Now, without knowing anything about the size of the school or numbers of people involved or layouts or, indeed, how well they manage the fire safety issues in the premises, I would not immediately say that their procedure is unsatisfactory. It probably is, but may not be if the premises are small and simple and very well managed.
If you do consider it unsatisfactory, then if they are having problems with false signals, maybe they should consider changing their system to a proper two stage one (could be expensive). If they are not troubled by false alarms then they should consider commencing evacuation immediately upon actuation of the alarm and conduct the investigation simultaneously with the evacuation.
Stu