The green wire should ultimately connect to batt neg.
the reg needs that connection as reference to the black wire to sense what the battery voltage is.
I don't know what your aftermarket reg uses for wire color and function.
I do know the the stock reg uses black as the voltage sense for the battery charge status and measures that voltage between its black and green connections.
The white wire on the bike goes to the alternator. The amount of voltage the reg sends to the alternator on this wire determines how much the alternator can deliver to the rectifier and ultimately the battery. At idle the white wire should get whatever is recieved on the black wire connection (battery voltage). When the engine is revved, the white wire varies with battery charge status, and the rpm of the alternator, due to battery charging.
The regulator you have should have come with wiring instructions. Or wire color function assignments. Care to share those?
How stock is your bike's wiring?
Cheers,