I believe the phrase "off your back foot" refers to which foot bears your weight when you take the action. It makes sense to me when shooting arrows, firing a rifle, pitching a baseball, golfing, or even bowling.
Remember that he said, "aim with your hips." This is common when aiming. Your hips are twisted to some degree to align with the target. This means one foot is forward (toward the target) and the other back (away from the target).
If your weight is on your back foot, the body is unbalanced and unstable. This will throw off your aim. (Give it a try, many people feel uncomfortable with their weight on a foot that's behind them.) If your weight is on your front foot, your body is stable and balanced, allowing you to steady your aim.