Tiled sprite doesn't fill the screen. It fills the widget's rectangle. When you move the widget, its rectangle is moved, so the filled area is moved as well.
You can change UVs of UITexture, but you can't change UVs of a tiled sprite. However if I understand what you're trying to do correctly, you can achieve what you want by simply making the widget wider, and when the tween reaches the end, restart it from the beginning. If you set it up correctly where the visible tiled area at the end matches the same texture at the beginning, there won't be any visible transition when it restarts the tween.