No, I think he has it correct.
The large (expansion) tank is under suction from the water pump fitting, via the connection at the bottom of the expansion tank. The air in the swirl tank moves out into the expansion tank - the swirl tank becomes a “de-gas” tank as it was originally designed.
My tanks are at about the same orientation (relative elevations) as you show…. When the system reaches equilibrium, the water lever in all the tanks will be the same (at the level of top of the swirl tank).
Rocky
Interesting idea to use the top overflow on the swirl tank, and mods to the gasket.