The reason for the family's absence is stated quite explicitly in the story, prior to the fire. The family was outside when a nuclear weapon was detonated somewhere nearby.
The house is introduced first, nearly as a character of its own, and clearly with a strong interactivity and dependence upon its family, but with an almost melancholy, but unhelpful, repetitive mention of their absence. The story provides no indication of their fate, nor how long they've been gone, until the outside of the home is described; the entire west side of it is blackened, except for five spots. Those five spots correspond to the silhouettes of a family, engaged in typical yard activities, suggesting that they were standing in that place, off-guard, and were incinerated by the blast.
In the broader context of The Martian Chronicles, it was foreshadowed in several other stories that a nuclear war was imminent, and that it consumed entire continents, which may help explain why not only the family was absent, but so was all other human life as well, and why no one came to check up on the family or influence the continued automatic operations of the house in any way.