This hum/buzz in the short moment you plug in the phones is completely normal and easily explained by the mains leakage currents of the stock supply.
A very simple experiment proves that right away:
- Connect the power-brick to the mains and to the ADI (on or off, doesn't matter), don't connect anything else (no source).
- Grab your phones plug at the shield portion of the plug and just touch the tip of the plug to the metal chassis of the interface, for example at the ring of the phones socket. A slight hum/buzz will be heard on the left cup.
- Now take a cable with alligator clips and connect that to the shield sleeve of phones plug and to PE Mains Earth (or earth-grounded water pipe etc). Again make contact to the RME's ground, this time holding the plug at the cable, not making any skin contact. The buzzing will be there again, and it will be louder (there is a more direct leakage path now).
- Finally, disconnect the RME from the supply and repeat the experiment, this time touching the DC-plug's outer contact with the tip of the phones plug. The results will be the same: buzz when your body skin is the return path, and louder buzz when a more direct return path is present.
In my case, using HD700 cans, this hum/buzz is very prominent.
With a source connected, things can change significantly. When the source has its GND connect to PE (3-prong mains plug), the hum will be (mostly) gone (the leakage current will take this path and won't flow through the phones), but when it is also powered from a high-leakage SMPS power-brick (the typical Laptop/Netbook supply) the effect can be softer or louder, depending on the actual electrical circumstances.
Fortunately, there is nothing to worry about because that is not a regular operating condition.