The residual sugar in the cider will ferment, as will the sugar added to sweeten the cider. It doesn't matter that the apple juice is pasteurized, as long as there are still yeast in the cider you're adding it to. To have a sweet cider you need to remove or kill the yeast before you sweeten.
You can use filtration or chemicals (potassium sorbate and sulfite) to kill or remove the yeast. I don't like these options since they both change the flavor. What I do is cold-crash the cider, which reduces the yeast's activity, though it doesn't kill them. I then carbonate and sweeten, always keeping the cider very cold. If you drink it quickly it probably won't re-ferment.
You could try cask conditioning to carbonate the cider, then cold crashing and back sweetening. Just be sure to keep the cider very cold after sweetening.