It sounds like gyroscopic optical image stabilization. Since a point and shoot requires using the screen all the time, it may leave the stabilization engaged. You can reproduce the same thing when you put a DSLR in LiveView mode if you choose the proper settings. When you go to review mode, the display isn't coming from the sensor, so the stabilization is not needed.
Basically, little tiny gyroscopes start spinning in order to make it so that when you rotate the camera, one of the lens elements keeps pointing things in the same direction. If you are looking at the screen to point the camera and it wasn't doing it, the view would be far more shaky. SLRs don't need to provide the stabilization when looking through the viewfinder because we are much better at working around any movement because our eye is moving with it rather than seeing movement on a stationary screen. Even so, when you half press the shutter, the stabilization will kick in on most DSLRs (when using an OIS lens).