I don't have the torsen, I have LSD in both my 1500 and 3500. The LSD's will "lock" under a certain amount of torque. If you apply that amount when starting out (certain amount of throttle applied), and you're starting out straight, and then turn, either left or right, you are going to notice the inside tire hopping/spinning. Usually more noticeable when turning left. When you are at a stop sign/light, and are going to turn right, most of the time you stopped with the truck angled toward the turn, and the front wheels turned. As soon as you start out, the rear wheels are already turning at a different speed, making it less likely to "lock".
I have noticed that I get more tire wear on the rears unless I do the following. When starting out, if I'm going to turn, I do a couple of things. First, I try not to apply too much throttle all at once, and when I do, as I go into the turn, I let off of the throttle a bit, hopefully unlocking the rearend, and slowly apply the throttle again once I'm into the turn and the rear tires are then turning at different speeds (due to the size of the arc they are following). If you notice your inside wheel hopping/spinning, let off of the throttle, thus decreasing torque, and hopefully it will unlock the diff.
As others have pointed out, you have 4.88 gears, which is going to exaggerate your problem, making it way more noticeable. Just like it's easier to spin the tires with lower gears, it's going to make it even easier to spin one. And the fact that you have lower gears, you have thus multiplied the torque applied to the rears at any given throttle, making it way easier to lock up the diff.
