I have several AC adapters that gives tinkling feeling to my hand when I accidentally touches its output.

The following image shows a typical circuit where there is a capacitor bridging the primary HV side and the secondary LV side.

http://www.st.com/stonline/books/pdf/docs/9682.pdf

I think it has something to do with EMI suppression but touching the output gives tinkling feeling to the back of my hand and there is a relatively high voltage when measured by a DVM w.r.t. real ground.

Why is this capacitor needed and what about the safety implication should this capacitor fails? Why go to HIPOT 5000V testing of the transformer and then ruin that by adding this capacitor?

Secondly, in the ST application note(shown below), is the DOT(polarity) of the HV transformer secondary output winding wrongly labeled? I asked because the explanation by the designer on how the circuit functions indicate it is of a flyback design.

 

I'd worry a lot more about the electronics connected to it myself. The transformer and optocoupler have it nicely isolated. It sounds like you have some high voltage spikes coming from somewhere.

Schematics like that give me a headache, they are so convoluted. What is coming out of the transformer would be an inverted waveform, but it will be AC. This means the rectification and filtering should do it's job.

As near as I can tell it varies the frequency of oscillator to send power to the other side. With only a little load (and most of it internal) an occasional pulse would do it.

Any way of getting an oscope shot of this? Approach with caution, I knew a guy who zapped 3 DVMs trying to get a reading of a 600VDC power supply. Near as we could tell it had some really high voltage spikes (with current) riding on DC (probably normal to the operation of the design). It would start the MOS conducting, then follow up with a massive surge of current. The inside of all 3 meters were melted, beyond all recognition. I sent one to a cal dept. as a joke. He wound up using a Simpson VOM to do the job.

My point is humans can survive a static equivalent zap with no problem, whereas an oscope front end might not be so lucky.

 

Looking at the print there are several anomolies. It defines that all caps are 50V unless otherwise specified. Problem is, the primary side of this design is going to run into hundreds of volts, possibly as high as 340VDC. C1, C2, and C12 have no voltage designations. The input to the circuit is undefined, just L and N, which to me means Line and Neutral, in other words, direct line voltage input.

 

I particularly like C1 as an electrolytic across an AC line.

I would guess the C8 is simply a spike remover. Since the secondary is floating with respect to the input power, polarity does not matter. The rectifier diode and ground connection will determine the polarity of the DC out.

Seems like a lot of trouble for 12 volts DC @ 840 ma. It's doubtless more efficient than a linear supply, and certainly uses lots less copper.