It's the "Lee Wulff" grip. I watched him demonstrate fly casting many times at numerous confabs. He could lay out 90 feet of line effortlessly with it. Sometime he kept his finger straight and sometimes he bent it. I watched him closely because that is the style I have always used. Never did get that 90 feet with it though! I tried the thumb on top but never felt comfortable with it. The rod grip kept twisting in my palm and next thing I knew the fly reel was horizontal instead of vertical. It helps your accuracy on short casts too. Not many people use it. I think it is a natural thing with those who do. There is no reason to stop doing it if it feels natural to you. When I played golf I also putted with my index finger held down along the shaft of the putter.
Cordially,
Bob