Battery or alternator?

[Az07Ford6.0]

Ok I recently installed a scangauge. My volts KOeo are showing 11.2-11.5. Once started and alternator kicks on volts jump to high 13's. I assumed he batteries were no longer holding charge. Well tonight I stopped by autozone on my way home to have Batteries tested. Dude said both batteries are showing 12 volts but that my alternator was bad. That don't make sense to me. I am here to ask the pros what u guys think, ps no engine or battery light is on

[southend]

Read this.....Bad alternator?

Sent from my phone that somebody didn't help me get.

[southend]

And this.....since battery voltages and cold weather are the discussions read..

Sent from my phone that somebody didn't help me get.

[Az07Ford6.0]

Thanks man this explains a lot