I also experience this anytime someone I know passes away. I always feel weird about it too, like I’m not doing the socially acceptable thing. It’s not that I don’t have emotions or care, I care a lot actually. I think people like us process emotions differently, I don’t usually have the ability to express them externally.
I am also an aspie and the way I think tends to be blunt and logical. So when it comes to death and things that are out of my control I just tend to accept it as a part of life, like it sucks to lose someone but imo letting it consume you is much worse than just being stoic about it. I hope your family comes to understand, I think remaining calm could be a sign of emotional strength actually!