I’m actually impressed that they have a home sprinkler system. And that it operated correctly. They are designed to wait until there is enough heat coming off the source before they active, to rule out false alarms and soaking your shit by accident. While the family basically contained it before hand, the steam from the water was that last crack of heat that sprinkler system could take before going off. That steam is hot AF too - I’m a paramedic/firefighter so I can tell you first hand how much worse a steam burn is.
They do not have a home sprinkler system at all!