To expand on Hanno Fietz' answer: I agree that the sound is caused by cavitation.
Does feathering the surface prevent cavitation? I don't think it does, I think the cavitation is still occurring.
Remember, the wand is blasting out pure steam, so if you submerge it into the milk before you turn it on, the steam is going to rapidly condense back into pure water with no "air" in it. This steam collapse is one form of cavitation.
As a liquid, milk (like water) is incompressible, so with no shock absorption the cavitation energy is transferred directly into the sides of the container. That is the sound that you are hearing, the cavitation energy "ringing" off the sides of the container.
However, by feathering the surface the steam will capture some atmosphere and introduce it into the milk as tiny bubbles. I think these tiny bubbles act as a shock-absorber for the energy of the cavitation. You can still hear the cavitation, it is just much more subdued because the air bubbles absorb most of the energy. The more you feather the surface, the more bubbles introduced, the quieter the cavitation noise.
Here is a demonstration of the power of cavitation:
I should point out that this video presents a different kind of cavitation, but it is the same idea.