I created both of these videos with Adobe Photoshop and Apple Motion. In Photoshop, I separated the layers, and then I animated them in Apple Motion.
For the 2-part animation, I simply clone-stamped the background layer in Photoshop prior to importing into motion, and then I used scaling to create a 3D effect.
However, in the 4-part one, I only separated the layers in Photoshop. In Motion, I separated each separate layer in Z-space. I then moved the camera to make it appear 3D. I also added a Throw behavior to the top sky layer.