rnwld's theory sounds right on. You should be seeing something like 13.5V at the battery with lights, blower and rear window grid all turned on and the engine at (say) 1500RPM. As he said, have the alternator checked again at a different store.

I took my pick 'n pull trophy to our local Shuck's auto parts store...the verdict? "no output, er...looks like bad diodes, this one's dead." Took it down the road to another Shuck's. Exact same machine, same cookbook for hooking it up. Verdict: "Lots of amps at 14V, this one's fine." The difference - only one of those guys knew what he was doing.

But if the second test duplicates the first (only 13V at light load), your alt. needs some work. New brushes and regulator assembly aren't expensive and easy to DIY.
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Bob (81-244GL B21F, 83-244DL B23F, 94-944 B230FD plus grocery-getter Dodge minivan, MGB, and numerous old motorcycles)

I assume you are measuring these voltages at the battery?
The bench test seems to indicate a problem, either with the test or your alternator. 13 volts is too low to insure keeping everything going and still charge the battery. Once you throw in some cable losses this would be marginal.
Was the 13 volts with a typical or light load, say 10-20 amps? or was this at full load, and did the tester set up the tester correctly for your alternator?
If too high a load was applied then the alternator could have read only 13 volts.
However, assuming the test was performed correctly 13 volts is out of spec for the alternator.
If you would like to assume the alternator is OK for now, you should check the voltage at the back of the alternator. This should be about 13.8- 14.2 volts with a light load (engine running, no lights, wipers). If it reads higher at the alternator than at the battery by more than 0.3 volts you have a poor ground of the alternator or a corroded or nearly broken wire to the battery.
The battery voltage will typically start a bit high and drop as you drive. Intially the battery is discharged and cold, the alternator will apply a higher charge voltage and drop about 0.5 volts as things warm up.

I have gotten vastly different results having my alternator bench tested. Take it to more than one place.
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744-16v,745-16v,242Turbo.245DLT