I'v never ridden a segway, so I really can't tell the specifics of how one balances on it, and I imagine folks who do balance on them wouldn't be able to say much more than that they do.
I know that on riding a bicycle, you can do an emergency turn by quickly steering the wheel towards the obstacle and out from under the CoG to induce a tilt away from the obstacle, then turn sharply back underneath the tilt to recover onto a new course away from the obstacle. https://www.youtube.com/watch?v=aNlYHg52LCM I imagine the dynamic balancing act on a segway has similar behaviors.
Even so, it isn't easy to understand these systems because they shift between inertial and non-inertial reference frames, and the simple words "tilt", "balance", "equilibrium" and even "angle zero" or "moment force" end up loaded with confusing assumptions and intuitions.