Power adapter outputting incorrect voltage
This is typical behavior for an unregulated AC transformer coupled wall wart that has just a rectifier bridge and filter capacitor. What you are seeing is the no load rectified voltage with no load. The output filter capacitors charge up to the peaks of the transformer output sine wave signal minus the two diode drop of the rectifier bridge. 

The 10-12V output will be more typical of the output voltage that you would measure when the full rated load is placed upon the output. In this case the measured value is the average voltage as supplied from the filter capacitor which is charging during the sine wave peaks and discharging between the peaks as the rectified sine waves go to zero.