Even if people absolutely didn't care about one's wellbeing (or even if they were bullies), they might still act like they miss that person dearly after death, because they - consciously or not - want to feed their ego. They may falsify their memories and actually start to believe that they cared for said person this whole time. Also, mourning makes them feel less guilty of the death and more proud for caring about the memory of the deceased. Other people also assume that they were probably close with the person who passed away, so they treat them with more respect and empathy.
I know that when you plan to ctb you may start to worry about those people's feelings, even if your rationality tells you that they never cared and so you shouldn't care about them either. But if those people really, really, REALLY don't mean anything to you, just as you never meant anything to them, it's worth to try to get over these worries. Don't let the fear of hurting someone, who doesn't deserve your sympathy, discourage you from doing what's best for you.