I'm not a Christian, but I know enough about Cjristian mythology to know that this is a gross misrepresentation of it. Satan isn't really supposed to punish sinners. He makes people sin - in essence, by "tricking" them into it (the prototypical example being Adam and Eve). He's not Hades. He just rules over hell because he's the ultimate sinner, the one responsible for the existence of sin and Hell.
Once they're in Hell, I've never heard of any Christian theology that claims that they undergo tortures, etc at the hands of Satan. Just being in Hell is their punishment, and its God who gives it to them, not Satan.