It has been claimed that activating the fire alarm pull would not set off the sprinklers, it would merely trigger the fire alarm to sound and also if equipped alert emergency services.
Sprinklers are activated by the heat of the fire and only the ones that the heat triggers are set off, not all of them at once.
However, that is not the only system and it would do nothing to protect the school full of children or the irreplaceable, largely flammable antiques. So in a place where teenagers are performing rituals with lots of candles and it's entirely possible to have "Firestarters" (pyrokinetics) as students, it would make sense to have a system (that exists in real life too) where pulling the alarm activates the sprinklers in the entire room.
At about 1:48, when Thing is photocopying a copy of the autopsy report, the first page when blown up says "County of Los Angeles" and "Department of Coroner." At the Beginning of the episode the morgue is identified as "Jericho County", "County - Medical Examiner" on the sign outside of the morgue..