Without a sufficient load the output will read higher than the rated output. Your multimeter by itself doesn't present enough of a load, so you need to measure the output when the adapter is connected to something. It could be something as simple as a resistor; a 1000 ohm 1/4 watt resistor might be enough.
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This is due to the voltage AC is a SINE-WAVE. When the diodes "flip" the sine wave UP above the zero line.... you can see with an OSCILLOSCOPE that the AVERAGE heating power of the waveform is 12 volts. HOWEVER the PEAK voltage (from zero to peak) is 18 volts. If you place an electrolytic capacitor across the terminals, the capacitor will charge up to the PEAK voltage which is 18 volts. To get that down to 12 volts, you need to put the voltage into a voltage regulator such as a ua7812 regulator chip. ANOTHER way of looking at this... is to think about the SHOCK value of electricity coming out of the wall outlet. If you got SHOCKED by the wall outlet by touching the wires... you would FEEL a PEAK voltage of 169 volts... but your finger would be "warmed" by the AVERAGE voltage of only 120 volts.
Probably because its an unregulated 12V supply, which because of the way they work will put out a nominal 12 x 1.414 volts, or roughly 18V when they are unloaded. If it matters, that's why you use a regulated power supply.
+1.When they aren't under load, they go out of regulation. Many low cost supplies work in this way. Try the measurement again, with a 1K resistor across the supply. Often times, even a small load (in this case approximately 10-20mA is enough to bring the feedback loop into focus. If that's not enough, then hunt down a 1W 220 ohm resistor and try it again or connect a small 12 motor and measure the output voltage with the load applied. It may not go to exactly 12VDC, but it should get close.