The world of Greek mythology is one where anything can happen, and often does. Gods and goddesses, who represent everything from agriculture to beauty to the sea, roam far and wide, causing drama among themselves and among the mortals. It's pretty much a series of ancient soap-operas; the poem doesn't even begin to touch on some of the crazy stuff that goes down.
For instance, Persephone's father is Zeus, god of thunder and causer of frequent trouble. He's pretty much the most powerful god of all, and he has a backstory that would make your head hurt. His brothers, Poseidon (god of sea) and Hades (who we already have the pleasure of knowing), were born of the same father, one that tried to eat Zeus before he was born. And don't even get into his relationship with his sister, Hera… We digress, but it seems like that's always the way with Greek myths. And it's in this world that Demeter and Hades exist.
Of course, Dove isn't just addressing these mythological deities; the poem addresses us as well. In our world, selfishness and anger play as much a role as they did back then. We, too, suffer because of the actions of others. More to the point: we, too, sometimes forget to think before we act. So, in the end, if you take out the supernatural powers, the poem's world isn't that dissimilar to our own. The true setting might best be understood, then, as the rocky terrain of human interaction. Watch your step, gang.