I have a hard copy of those carburetor instructions but no good electronic copy at this time. The diaphragm in the fuel tank is the fuel pump, the large diaphragm in the carburetor body is the metering diaphragm. As Stephan noted, the 33/35/39 carburetors use a ball rather than a needle in the metering circuit.
If you play with it a bit you will see that when you open the throttle, is also lifts a push rod that admits more fuel; similar in design and operation of the McCulloch -10 Series flat back/bullfrog carburetors. The low speed adjustment is controlled by the metering needle in the bottom of the carburetor and the high speed adjustment by the lever in the top which actually limits how far the throttle is opened, controlling the rod that meters the fuel. Adjust the metering needle in the bottom to achieve a good idle then adjust the lever to run just slightly rich at high speed. Every 33/35/39 saw that I have run will never clean up out of the cut so they evidently designed them to run on the rich side.
You will discover that they are extremely reliable starting and running saws, yes they run pig rich and yes they are slow as molasses in the cut, but they do start and run. See your PM for some additional information.
The metering diaphragm, lever, and ball seat - note the lever is shown in the wrong position, the tab will be one the end of the diaphragm to hold it in place
The bottom end of the carburetor and primer
The bottom end of the carburetor and the low speed needle arrangement
The fuel pump in the tank - first photo is the fully assembled pump minus the filter
And all the parts in order...
Add the fuel filter/wick
More to come...
Mark