1991 Toyota 4Runner Alternator and/or regulator

Both brake and battery lights came on and was advised that this is an alternator issue. I charged my battery as advised and then replace the alternator with a reman. Lights were still on. I set the charger for a slow trickle charge for the night, then started the engine in the morning. Lights were still on. Used a multimeter to check output. Voltage was slowly coming up from 12.5 to 12.85, then a click and jumped to 14.2. Checked lights and they had gone off, but then came back on. Is this a regulator problem? I notice on one of your posts that this vehicle has an internal voltage regulator. What does that mean?