Classic/Antique Car Repair: Generator running off battery, ford galaxy 500, 1963 ford galaxy 500

Question
I have a 1963 Ford Galaxy 500 equipped with a generator.  I threw a generator belt today and when I turned the ignition off the generator light stayed on.  I popped the hood and found the generator was spinning.  I disconnected the battery and it stopped.  What is going on?  Surely this can't be normal.  Also I just replaced the generator with a new or rebuilt one, the old one has 2 pullies on it and the new one has only one.  I was told it needs to have 2 pullies as the generator turns harder than alternator and needs 2.  Is this true?  Thanks

Answer
First of all, the current cut out relay points are sticking in the voltage regulator. These points are supposed to open and disconnect the generator for the system when the charging voltage of the generator drops below battery voltage. As for the double belt goes the load on the belts is the same in both the alternator and the generator at a given amp output. The pulleys are easy to change if you still have the old generator. If there was two belts when the car was built I would suggest that two belt be used now and it has nothing to do with alternator vs generator.