Did you have your original alternator tested? From what you describe I am not sure you need a new alternator. The big red wire on your alternator goes straigt to the starter. The battery and the rest of the car only get power from the alternator from another big red wire that goes from the starter to the battery. Since the problem started when they changed the starter I would check this connection. If this connection was not made properly you could have burned out your voltage regulator. Even if your alternator is broken, they can usually be repaired for less than 100 bucks. Its often just the brush/voltage regulator that goes. Thats way cheaper then what you paid.
The ground wire connnects to the body of the alternator. There may be a specific screw on the housing for this, or it may be attached to one of the bolts that holds the alternator together. It does not really matter as long as it is well grounded. The big red wire usually attaches to a large threaded post. You can identify it because it is insulated from the rest of the alternator. There should be a non conductive washer under it (plastic usually). The small red wire usually hooks up to a spade connection that is recessed inside the alternator. It is recessed because the connector is on the "diode" assembley inside the back. I have never seen a fourth terminal on a Volvo alternator. It sounds like the one you got is a generic alternator not specific to Volvo.