The air on the upper surface accelerates because the air is compressed by the greater surface area which can be created either by camber or AOA or a combination of both. (The air is essentially squezed much like when you squeze the end of a water hose to make the water come out faster.)
Area x velocity = constant
In this case the area is reduced by the camber so therefore the velocity has to increase.
Static pressure + dynamic pressure = constant
We have now increased the dynamic pressure of the air so therefore the static pressure on the upper surface is reduced, creating a net pressure difference between the lower and upper surface. Net result is a lifting action.
The wing tip vortices are caused by the higher pressure under the wing trying to equalize with the lower pressure on top of the wing as it passes through the air.