Okay, I've written a script that will resize and position of the parallax background automatically, regardless of the screen's and sprite's resolutions and orientations. You can get it here.
1. Create a TabView.
2. Make the alpha on the Image on the TabView object 0.
3. Set 'Show Graphic' on the Mask on the Tab Bar to true, and set the Image color to the desired color.
4. Set the alpha on each tab's background image to 0 (It's important to keep the images there or the container will not scroll).
5. Add an Image under the Pages object, but above the Container object in the hierarchy (so it is drawn behind the Container). This will be the parallax background, so set its sprite to your desired background sprite.
6. Add the attached script to this new Image, and set the Container Rect Transform value to the Container object's RectTransform.
8. The parallax image should now resize and position itself accordinly in both edit and play modes :)
Let me know if that helps!