How's it work? I can think of two things, one being that the discharge formed at the probe makes enough UV to decrease the striking voltage, like the UV enhancers in modern pulse-start lamps except in the lamp. The other thing I can think of would be some sort of barrier being broken around the main electrode to lower it's striking voltage, and I guess it is only necessary to do that to one electrode to get sufficient striking(?). Anyone know?

To start a discharge, you need electrons that can move between electrodes, pick up energy and when hitting atoms kicking out another lectron, so generating more of free particles. Mainly on the cathode side.
The auxiliaru discharge generates it on its own directly (when on the cathode side) or indirectly (via the UV emission, illuminating the cathode on the other side and kicking out of it electrons by the photoemission).