What tone, or attitude, does the automated voice use to address the missing inhabitants?

The voice or tone of the automated home system in addressing the "inhabitants" is neutral and not conscious of the situation. The inhabitants—two adults and two children—have died a long time ago during a nuclear explosion. However, the robotic home system does not know this, as the system is not an artificial intelligence system that can analyze situations and "think."
The neutral, non-human tone of the automated home system is meant to convey the separation of man and machine. Humans, such as those who once inhabited the house, have become dependent on technology, but they can never have an intimate relationship with it the way humans and animal pets can interact.
In fact, the family's dog is the only member of the household that survives. In this context, the automated house represents one form of human-nonhuman dynamic, and the pet dog represents a different kind of human-nonhuman dynamic.
The automated system's language and monotonous tone is out of place in a house that has experienced tragedy—that is, the death of the family—and it shows technology as machines out of touch with the human condition.
The neutrality of the system's tone and automated activities also epitomizes the old saying "life goes on." In this case, life literally moves on after the death of the human occupants, until the dog and the system itself die.