It's not a spool or Detroit Locker, it's a limited slip differential. We'll assume that it's full of engine torque and has enough power to make a habit of spending tire money for little return, but the bottom line is that you're making enough multiplied TQ to put the differential to work. If you have a positraction (limited slip) with 1 tire on snow or ice, apply light throttle pressure, you'll simply drive away. Stab it to the floor and you'll burn right through the differential action with no effort, spinning the tire on the ice as if it were and open diff in a regular car. Let's add another "twist" as well, that is the twisting motion of the axle when power is applied. Looking at the car from the rear, the axle has a natural reaction when TQ is applied heavily to rotate counter-clockwise. In simple terms, it wants to lift the right rear tire. So many go through their car life thinking the left rear tire is the "traction side", when in an open rear diff it's whatever side gets enough weight to do the work. You can make an open diff spin both wheels in some conditions by how you place the car. Hang the rear to the left a bit as you line up, not much, just a bit. When you stab the gas the car shifts extra weight to the right rear, this in turn counters the TQ reaction of raising the rt rear tire.
Short version? Your "posi" is most likely working just fine in normal operating conditions. G.M. didn't design those to work on drag strips with excess traction conditions, nor to be able to paint black lines in urban pavement. They're a traction aid giving an advantage to both rear tires in unequal conditions.