The domain of a utility function is possible states of the world. The whole world, not just the parts you can physically affect. Some utility functions (such as total utilitarianism) can be factored into an integral over spacetime (and over other stuff for Tegmark IV) of some locally-supported function, and some can't. If you have a non-factorable utility function, then even if the world is partitioned into non-interacting pieces x and y and you're in x, the value of y still affects ∂U/∂x, and is thus relevant to decisions.