Adj vac advance on factory dist.

Adjusting the spring either compresses it or reduces the tension. If the Allen screw is fully CW, less vacuum is needed to move the actuator compared to when the screw is would a few turns CCW. So the Allen screw affects spring tension, which in turn affects the amount of vac reqd to move the actuator.

Exactly. And no matter how you try to explain it, someone always thinks the opposite. That tightening the adjuster screw makes it take more vacuum to work. It's just like you said.
I think what gives people the most trouble is that it works backwards from conventional thinking. Tighten the adjuster, less spring pressure, less vacuum needed to start movement. Loosen the adjuster, more spring pressure, more vacuum needed to start movement. The picture posted by @halifaxhops makes it easier to visualize how the spring cup moves with the adjuster screw.