From the operator’s perspective, a single push is understandable. Presumably pushing the button triggers an audible and visual alert on the operator’s end, and it would be annoying and distracting to have that repeated (much like persistent phone callers ringing multiple times in a row).
However, from the point of view of the user (the person in an emergency), I find such a request unreasonable and indicative of a pretty basic misunderstanding of the concept of an emergency.
Heightened tensions, lots of action, a need for rapid response.
And yet, despite all that and notwithstanding the particular challenges of the specific situation, the designer of this system is asking that the user take the time to read instructions and also wait patiently for a reply.
No, it’s not horribly unreasonable, but it does seem like the kind of thing that could easily be understood about the intended product use scenario and then designed around.
If you push twice, will you not be helped? What will three pushes get you?