Alternator testing bad with ac on but testing good when it off

Today I decided I wanted to grab something to eat with my brother and drove 15 mins to a place to eat and parked my car for no longer than 15 mins went out back to my car and battery was shot. I got jumped and the car drove 15-30 mins to the place to get a new battery. I also got the alternator tested and my ac was on and it read 13.45 Volts and with it off it was in the green. I don’t know if I should replace the alternator or just run it? Car is a 2013 Camry Se