To provide more information than the others who responded: typical sprinkler systems are not automatically activated in response to a fire alarm. Each sprinkler head has a small glass vial filled with a liquid, calibrated to break at a certain elevated temperature (e.g 160 or 180 F). The flow of water starts when the glass breaks. So there has to be a significant fire near the sprinkler before it activates.

One weakness is that the glass vial is fragile. In some hotels you’ll see signs reminding guests not to hang clothes from the sprinkler head, as a clothes hanger could break the vial and activate the water flow.