Probably need more detail, but my guess is you have a bad mesh. If you click the little mesh icon in the “rig” panel or “scene” panel, it shows a yellow mesh of how everything hooks up. If all is well, you will see the yellow mesh maps to the outline of your puppet nicely. But sometimes it cannot understand your artwork and uses a rectangular mesh where everything is connected. Then moving an arm moves the body as well. Independence of different layers also can come in here.
If the auto mesh is wrong, you can manually pick “contour” which is generally correct. It normally gets it wrong if you have unconnected bits of artwork (even if a single pixel!) - it throws up its hands in such cases sometimes.
But my first suggestion (from the helpful Adobe folks) is to turn on the mesh first and see if you get a hint what is going on. A recent similar post was Distorting face bug in case useful. Otherwise search the forums for the word “mesh” and you might find more hints.
Did alank's suggestion help at all?
Let us know.