Capacitor changing output voltage from 12v to 20v
Without a filter capacitor, your meter will read some form of average of the rectified waveform, which will vary from Zero to the AC peak voltage every half-cycle.

With a filter capacitor, and little or no load on the power supply, the capacitor will charge up to nearly the peak AC voltage, and will provide nearly pure DC at that voltage, causing your meter to read a higher voltage than it did without the filter capacitor.