There's two possibilities, and it could both.
1. The battery was low on charge. Even with the alternator regulated to 14-14.9 Volts, a very low battery will draw over 40 amps if the alternator can supply it. Once the engine is revving at 1500 rpm or higher, its going to be getting close to being near its rated capability.
2. The alternator output voltage is not being properly regulated. One reason could be the field wire returning to the regulator is grounding (shorted)
Another reason can be the sensing wire is reading low (diconnected , broken wire, or resistance in the supply lines). The resistance is why checking for voltage at key locations is important. When there is a more current (moving electrons) then any location where there is resistance is going to cause a drop in voltage. If the regulator 'sees' 13 volts when the alternator is producing at 15 Volts, then the regulator is sensing low voltage, and will continue to create a field until it sees the 14+ volts. That might mean the alternator is producing at 16 volts. The battery might be seeing 16 volts, or might be seeing 13 volts. it all depends on where the resistance is, and where the current is going.