That means that most likely an infrared sensor won't be able to tell the difference between people and surrounding warm/hot objects.
PID sensors register movement of bodies with a temperature different from ambient perpendicular on their two windows, simple as that.
If the garden bench get hot and runs toward the sprinkler, perhaps it's because it needs a chill
Also, after you pour water on a kid, he won't register anymore as warm. Which will disrupt the readings of the sensor.
That would require massive amounts of water and if the kid actually got colder than the surroundings (highly unlikely), a temperature difference would still exist.
PIR devices with Fresnel lenses can be had covering a narrow or a wide angle 90° to 120° is easy to get and would then require 3 or 4 for a full circle detection and assuming lots of kids running around, perhaps it would be more sensible to open the water valve (or increase pressure) on detection, rather than trying to control the direction of the water, as it would be quite expensive with eg. 10° zones (and hard to get btw.), and if kids come from every direction, then what?
If the ground around the water area is somewhat controlable, sensor wires could radiate out from the water gizmo - capacitive sensors might be hard to use, due to the ground effect, but piezo wire should be good (although quite expensive).
Another thing to consider is, that it need to be totally water proof
- and don't include mains voltages
or things may go really bad.