The light does not need resetting. It goes out instantly as soon as the fault is fixed. If the alternator is charging correctly, then it sounds as if the problem is with the wire that connects the alternator to the light (or that the alternator isn't compatible, or has an internal fault which causes it to send the wrong diagnostic signal).
On the IS220, the alternator the light is controlled by the blue/black wire from the alternator which runs to the dash. If this wire isn't connected, then the light will come on, or if the alternator is putting the wrong voltage on this wire, then the light will come on. It should be fairly straight forward for an auto electrician to check if the alternator is putting the correct 12 V signal on this wire.
On the IS250, the alternator communicates with the ECU directly, and the ECU communicates digitally with the dash via CANbus. In this case, there is a red wire running from the alternator to the ECU which carries the "alternator working correctly" signal.