The alternator light is just a simple circuit connected directly to the alternator. For the battery to charge, it must have a higher voltage connected for current to flow through it (which gives the charging action).
The alternator light is isolated from the rest of the vehicle (battery) circuit by a diode. If the voltage from the alternator circuit is lower than the battery circuit, then the light turns on. That indicates the alternator is not producing sufficient voltage to charge the battery.
The voltage meter basically indicates the battery voltage, whereas the alternator light gives a simple indication of the alternator voltage. Usually, you don't need to know the exact voltage produced by the alternator -- you just need to know that it's a little bit more
than the battery voltage. That's why it's just a light.
From what you've said, the battery seems to be charging alright -- the voltage with the alternator connected to the battery is 15.2V, and lower when not running, 12.95V.
Don't know exactly what the alternator harness looks like on a '98, but there should be a seperate alternator light wire -- smaller gage -- that goes directly to the voltage regulator inside the alternator. In my '07, it's gray. Your's might be a different colour. Check that wire and it's connector. Maybe it got damaged installing the new alternator.
What kind of alternator did you put in? Is it a new one? If it's remanufactured, the voltage regulator could be borderline. The voltage regulator module provides the alternator light signal. Does the voltage you measure with your voltmeter vary significantly as you rev the engine? It shouldn't.
With road salt, 12 Ontario years are worth 25 Alberta years on electrical systems.