Multimeter XL830L: How to know if it is AC or DC?
Good that you included a link to the manual. The lowest ACV range on that multimeter is 200VAC so it seems they've just used a series diode to read the AC voltage rather than the more usual precision rectifier, thus saving a few pennies.
The average voltage of a half-wave rectified sinusoidal waveform of x volts RMS is about 1/2.2 (\$\sqrt{2}/\pi\$ to be exact) times x, so they need to jig the reference lower by that ratio to make it read higher (to approximate the correct RMS reading on the display. That accounts for the higher reading when DC of the correct polarity was applied- also the diode drops a bit of voltage so it will be closer to (Vin(DC)-0.7)*2.22. That increasing inaccuracy at low voltages is why they don't provide a lower AC range than 200VAC. With 10V applied I get a predicted reading of 20.6, close enough.
If you had reversed the leads it probably would have read zero.
Don't believe everything you read on the internet (including here). Many multimeters are as described, but not all.