It's really both. Figure 8 in the paper depicts this circulation theory of lift. The top and bottom surfaces interact via this phenomenon, though the top is more critical as the paper explains.

Also terms like "push" and "pull" really confuse the mechanics here. What matters is that a net upward force is being generated, with positive pressure acting on all sides of the airfoil. There is more pressure acting upon the lower surfaces than on the upper surfaces, but at every point the pressure is positive because it is surrounded by fluid (not in a vacuum). If you integrated the pressure acting on a lifting airfoil and computed the average direction, it would be pointed up.

Good point, if the top of the wing diverts air downward via reduced air pressure above the wing, then it would be the higher pressure air underneath (pushing) that creates the lift. Yeah, I can see how terms like "push" and "pull" get pretty confusing.