I just replaced the alternator in my 2013 Avalon also and have the same problem.
I'm reading about 14V at idle and the battery settles to 12.6V when it sits.
I don't see any bad connections.
Did you load test the battery too?
Ask your mechanic to load test the battery and alternator. The battery light should be off when battery and alternator work fine.
It's possible the light may just need to be turned of via the diagnostic (OBDII) port after replacing the battery or alternator, I have seen the same with those intermittent service lights too, no matter what work is carried out they usually need to be shut off via a scan tool.
Voltage sounds completely normal.
maybe the voltage dropped too much during cranking. You should probably just have your charging system tested professionally.
I'm still trying to figure out why the battery light won't go out.
My scanner doesn't show any faults to reset.
A mechanic friend has a commercial scanner that I can try though. Thx