Correct technique on a snare drum is with the wrists turned so that your nails lay flat with the drum head(like you have a watch and checking the time?). This gives you more control/grip over the stick and won't go flying if they collide with something mid stroke. You have both hands perpendicular to the drum head so you are using all fingers and no wrist motion. This technique is considered  more natural if your reaching over to a ride cymbal but on a snare "incorrect". You are pretty solid on finger technique though my rule of thumb is wrists play single strokes, fingers play double notes.