What would be an example of a macro process causing a micro without going through micro processes?

I would think the best you can do is something like fractal geometry, where self-similarity appears at all scales. In some sense, the rules are both micro and macroscopic. An example where this might have real-world implications is Palmer's Invariant Set Theory, which suggests that this fractal structure shapes both cosmological structures and what we see in quantum theory, eg. like violations of Bell's inequality,