+1, I think the rebuilt alternator has a bad regulator. There are a lot of things that'll drop the system voltage on a car, but only the regulator can fail higher than the usual 13-15vdc our cars run at.
You can take a shot at the CEL by doing the stomp test (you know...key to position 1, don't start the car, stomp the gas pedal five times in ten seconds). If it's on all the time, the car sensed a significant problem. Mine comes on every now & then. Usually it's an O2 sensor problem, often related to leak in the intake..