I'm still confused about what the center cylinder does.
It seems like it's part of the turbocharger, or at least that's what I gather.
For a similar setup,
check out this converted Ducati. This guy converted his V-twin into a single + an air-pump (supercharger).
After looking at the camshaft arrangement, I think I have an idea of what may be happening...
Notice that there is only one set of lobes per firing cylinder; the center cylinder has two sets of lobes, but we'll get to that later. Also, keep in mind that it is forced induction.
What i think is happening is that there is no separate intake or exhaust valves for the firing cylinders. The valves do double-time, operating as
both intake and exhaust valves. What dictates where the air goes is both the turbocharger and the air-pump/vac in the center (with its own set of valves, which operate as exhaust-only valves).
On the intake stroke, the turbocharger is forcing air in, and the center cylinder is closed off. Fresh mix comes in, and when the motor hits BDC, the valves close (could be past BDC through compression stroke, depending on the turbo arrangement). Then the firing cylinder goes through compression/explosion strokes as per a normal four stroke. As the firing cylinder goes from BDC to TDC on the exhaust stroke, the valves open, and the air-pump center cylinder acts as a vacuum and helps draw the exhaust gases out. Once TDC is reached, the air-pump is no longer used as the turbocharger is now back in charge of getting the fresh charge in. The whole time this happens the valves remain open.
Of course, this is all conjecture, speculation, and probably waaay off base on how it is really done.