When do you see evidence that there are civilian family members present? Was there an opening ceremony going on or something?
Garrison bases often do, forward operating bases generally don't, neither do warships. The death star is arguably somewhere between the latter and a gargantuan warship. There's at least a very good reason to suspect it wouldn't have civilian family areas.
Also, in a any case, at least the one destroyed in Episode IV was in immediate self-defense as the Death Star was imminently attacking the entire planet on which the rebel base was located, so there would be no duty to evacuate civilians even if the rebels had the theoretical ability to do so without the time constraints posed by the imminent attack, which they didn't—it’s not like they captured the Death Star and scuttled it with crew and any hypothetical civilian dependents on board.