changing position when changing scale

You have to use a specific part of the menu.  Don't scale from the Transform menu.  Go to the Animate Text submenu of Animation and use those to do your scaling, position changes, etc.  You can do your scaling without having it drift off its center.

Here's a picture:

The puppet moves relative to the anchor points. This is most apparent when the scale is changed. You can adjust the anchor points (usually the Y anchor point) in the Transform behavior in the properties panel. It's a little tricky because the anchor points are not visible, so it is trial and error. The easiest way I've found is to ignore the anchor points while recording, and then go to the end of the recording and adjust the anchor points to where you want the puppet to be at that time.