By definition it's engine braking. The lag in piston speed is what's slowing the car - nothing in the trans is doing it.
Every auto transmission is different, and now with computer controlled trans, each car can be different. An auto trans can either freewheel or engage the engine when the driveshaft is turning faster than the engine would be forcing it to turn through the trans. Traditionally, autos were set up to freewheel in the top gear(s) and engage in lower gears for downhill engine braking. But the engagement into the lower gears was usually very slow to make that nice comfortably feeling, and engine tuning generally let engines spin faster easily.
My experience was the same. Engine braking is a little more aggressive in the stinger, the downshifts are pretty sharp, and the engine is pretty stubborn about slowing down. It won't rev up when turned by the trans. I got used to it in about a month and don't notice now (or my right foot drives around it).