Which happens first, the zombie dying by despair or the spawn?
I would assume (but I can't find conclusive corroboration) that zombies would dies of despair BEFORE zombie spawning is calculated. It makes sense, when you consider the game mechanics... this is (weakly) supported by this page, which suggests that deaths from despair occur at '23.59' - ie before the attack - but this is hardly conclusive.
The zombies die of despair first. In your example of 12 zombies in a zone, killing 8 of them, the remaining zombies will in fact die before new zombies are spawned in that zone.