That kind of thing is typical of some converters.. NOTE that your volt meter may have been in error as well..
There are, for this discussion, 3 types of converters
One: Magnetek 6300, I do not think this applies so that's all I'll say about it, but I could be wrong, it has very poor voltage regulation and may give false readings on some voltmeters (Digital ones mostly)
Two: Poorly FILTERED Regulators. (NOTE this class also includes the one above) these may, and for the same reaons, give false readings on a digital meter They are designed to use the battery as a giant filter capacitor. They do respond EXACTLY like the O/P's
Three: Well filtered power supply/converters.. I have, from time to time, accidentally hit the disconnect on my batteries so I was running 100% on the converter.. My Kenwood TS-2000 did not notice the difference, far as it was concerned it had nice, clean 12 (Well 13.6) volt DC coming in the power lead.
On these the voltmeter will be as accurate as it gets for that meter. NO false readings.