Sounds right to me. Valve should be able to switch between starting gas tank and tractor fuel tank (that's two lines) and the 3rd one should go to carburetor.
I suppose there is an off positon where neither one flows to carb?
Just noticed that you said the line from starting gas tank comes out the top? Is there a line from the bottom of it into carburetor or change-over valve? Is there a return line fitting into the top of the tractor fuel tank as well?