Generators "self energized" in order to close the "reverse voltage" relay; which was the only way to keep the generator from "running as an electric motor" when the battery voltage was higher than the generator voltage. They used a 'mechanical' rectifier (ie the commutator) to convert AC to DC, and there was no (convenient) way to prevent the battery from draining through the generator once the engine was shut off. Their armature was a heavy 'block' of steel, which would retain residual magnetism, and when spun fast enough would induce enough voltage into the field windings to close the relay.
Alternators use solid state rectifiers (diodes) which electronically prevent "backfeed". Their field windings are what spin, and they are light enough that they will not impart significant voltage into the armature windings, which is a moot point as there is no need for a "reverse voltage" relay anyway. They require an external source of voltage (battery / jumper cables) in order to begin charging. It does not need 12 volts, just 2 or 3 volts to begin charging.
Typically, alternators can develop somewhere around 1/3 of their rated amperage at idle, and reach full amperage around 1,200 / 1,500 (engine) RPM.
Besides, I thought your problem was that it was overcharging??? (15.36 volts)