its difficult to not do that, you have to kind of roll the string around your hand or vice versa, its hard to explain. grabbing the string and just holding on is what causes the string to wrap up your hand, so you have to time your pulls along with letting go of the string to let it roll along your hand.
lots and lots of practice are what you need at this point. go with one round, then with two rounds until it feels good, then with three.... and so on until you can do as many rounds as you want. adding the fourth and fifth rounds become easier since you already have the technique down.