What you're doing there, or what it sounds like from your description, is called a Pinch Harmonic...you'll see it often in tablature as P.H. When the pick turns sideways your fingers are getting closer to the strings. I think every once in awhile you're hitting a harmonic with your thumb at the precise time you hit the string with the pick. This doesn't have to be done aggressively if you train yourself to know where the harmonics are in relation to where you're playing...infact if you do it soft enough it can even sound like a harp...