To answer the original question, the pulley on the generator of my '60 bugeye is 3 5/8" in diameter, measured at the outermost edge. However, it's hard to see how you could get the wrong size pulley, especially to give a reading of twice what you should get--it would have to be 2" in diameter! Also, if the pointer is bouncing a lot, that 2x estimate can't be very accurate, I suspect.
The cable follows a rather tortuous path between the generator and tach, and it can easily bind in the housing. Then, when it lets go, the pointer jumps, and maybe that's why it seems to indicate fast. Finally, if the pointer has been moved on its pin, that could cause the indication to be inaccurate.
I'd make sure that the cable is moving smoothly first--that might fix it completely.