I'll take a swing. I had my WC station designed somewhat similarly, but mine was vertical (RO on top, SW on bottom).
Tank on right is RO/DI. Tank on left is SW.
The valves at either end of the horizontal pipe seem to be extraneous - for "future use", perhaps.
The design on the left circulates water from bottom of tank to top to mix SW.
Close second valve from left, open third valve from left, open valve on vertical pipe and pump RO into SW mixing tank.
Close third valve from left, open second valve from left, leave valve on vertical pipe open and circulate water in that tank. Add salt...
Keep second valve from left open, close valve on vertical pipe, open valve connected to hose and send SW out hose.
Close second valve from left, leave valve on vertical pipe closed, open third valve from left, leave valve connected to hose open and send RO out hose.
Using the side by side design, I would think you would ultimately end up with some back flow of SW into your RO, but not necessarily enough that it would matter.