Actually turning your body early is good. This is CBM, and it should happen on step 1. However the change in your direction of motion - where you feet are going, happens later in the figure. Classically between step 2 and 3 for the more progressive 3/8 turn figures, but also between step 1 and 2 for the choppier 1/4 turn figures.
CBM is a preparation to change direction, accomplished by rotating the body while it continues to move in the preceding direction. Only later does the direction of motion changes to catch up to the one suggested by the CBM.
To do a reverse turning figure, turn your hips and eyes (but not head) first, start the step letting your shoulders turn as your take it, but place the first step in the original direction without much turn. Only subsequent steps will follow the body rotation to a new direction. To do a natural turning figure, turn your upper body first, then your hips.
You head tends to change its orientation at the same point in the figure when your moving foot does.