2013 Toyota Sienna - Alternator tested bad at Autozone, but voltage reads 13.9

Hi.  64,000 miles.  No start, weak crank this morning.  Put charger on van, waited 20 minutes, it started.  Checked between battery terminals with voltmeter, got 13.9.  Drove to Autozone because I figured it's a battery.  Asked them to test alternator.  They used tester and did their alternator test, told me voltage regulator is bad.  How trustworthy is that test?  If voltage regulator is bad, why does it seem to be charging (because of the 13.9 volts)?  I couldn't find a date on the battery.  We bought the van last year and battery could be original.  Does anyone know what the tester actually tests?  I'm trying to wrap my head around the alternator testing bad when it seems to be charging.  Thanks,
Jim

This depends very much on the tester. Obviously it will check charging voltage at different rpm and ac-ripple, probably amperage output as well.

How long was the van sitting for? Maybe a bad alternator diode causing a parasitic draw.

13.9 volts is lower than I like to see.
To test an alternator properly the battery has to be charged and then tested after the battery has rested for at least 2 hours.
Then the alternator charging voltage is checked under load normally that means headlights on main beam and heater blower on at medium speed. Normally expect between about 14.1 and 14.8 volts at 2,500 rpm on a petrol engine 1500 rpm on a diesel.
Low voltage can be due to a number of issues, slipping belts, worn brushed, bad doiode or regulator, bad high resistance in the main positive connection or ground wire.
With the engine at raised RPM switch off the loads and watch how voltage behaves any spike above 15v indicates a bad connection issue or faulty regulator.
The next check is for excess AC voltage ripple at the main alternator B+ terminnal this is really best carried out with an oscilloscope bit a multimeter meter on AC setting should show up a failure anything over about 0.3v is suspicious.
Checking for parasitic drain with engine off is the next test less than 30ma is ideal but less than 60ma won't normally cause issues unless the vehicle is parked for more than two weeks.

Weak batteries will very often send 'automated' charging system testers for a loop. :silly:

Especially Midtronics, or rebranded Midtronics. The excessive AC ripple generated by the alternator trying to keep up with the weak battery will cause the tester to flag the alternator as bad. Used to see it all the time when I worked at a tire chain.

I'll bet that the alternator section of their tester will pass after replacing the battery.