Get minimum phase from function
Why is it that reflecting any poles or zeros of a rational function across the unit circle gives a minimum phase system?

It doesn't. You are starting with a wrong assumption.

Here's an example, it seems reflecting any poles or zeros would result in the zeros being outside the circle?

Correct. Hence it's nonsense and you shouldn't do it. Assuming that the 'x' marks the poles, the system is unstable or non-causal anyway.
Roughly speaking:

A system is minimum phase if all zeros and poles are inside the unit circle.
A system with zeros outside the unit circle can be made minimum phase by reflecting the zeros at the unit circle
If have poles outside the unit circle, chances are something went wrong already and minimum phase is the least of your problems.