If it’s not putting out about 14.4 volts, then the alternator is bad. I don’t trust Advance with testing stuff, I had one of their batteries that died under warranty. I’m no noob, so I checked it, put it on my trickle charger overnight, tested it again, verified an internal short that was causing it to self-drain, left it overnight in the cold in the truck and took it to them to warranty after work the next day. They “tested” it three times and their “tester” said it was a good battery… I explained that it simply wasn’t possible as the battery had already froze into a block of ice (middle of winter). Took dragging their commercial manager out of his back office to confirm the battery was junk because it “tested” good.
Autozone also will test alternators and the like, I’d try getting some confirmation. I’d also inspect the wiring in the vehicle and check the main fuse under the hood.