Sorry but this source is pretty bad. The explanation is clearly wrong. You should download a basics aerodynamic book...
Here's what happen in a finite (real world) wing, the lifting of the wing generates a pressure field which induces vortices running from the lower surface to the upper, these vortices generate the downwash which is explicitly related to induced drag by a simple equation. The strength of the downwash is mainly depended on the lift coefficient and the aspect ratio of the wing, and in the limiting case of infinite wing (which is a theoretical aerodynamic's term) the wing's induced downwash doesn't exist and induced drag is zero.
So, downwash or upwash would depend on the wing geometry and lift, it's lift tha generates the upwash/downwash and also affected by it since it modifies the local angle of attack on each wing's section.
If you're considering the full airplane, the upwash/downwash of wing is also affected by the fuselage near the root.
This picture you posted is very wrong and confusing, because even in 2D flow, you have a cambering of the flow behind the airfoil (of course flow isn't just going flat after trailing edge). The flow then re-alignes with the freestream direction.

This picture. taken by a Stanford's Aerodynamic's lecture course, perfectly answers your question
The Kutta-Jukowski theorem for lift states that lift is proportional to density, freestream velocity and circulation $\Gamma$ by the equation $L=\rho V_{\infty} \Gamma$. For a 2D airfoil the circulation is as depicted in the far upper sketch and will produce an upwash in leading edge region and a downwash in the trailing edge region, then in the second sketch you see the downwash induced by the wing's free vortices. Lastly, you see the combined induced flowfield.