I think what you're talking about is promoting long term personal well-being - skillful action. Skillful action feels good.

Good point - if morality is about others, why do it? Where's the benefit for me? Because, like you say, what works for others works for me; and we live in a closely interdependent world, where what is good for you is good for me.

The version of utilitarianism that can be derived under this evolutionary paradigm specifies benefits for the self as well as others.