Sprite UVs are somewhere in the atlas. For example, a sprite can have a rect of (0.1, 0.1, 0.2, 0.2) within an atlas. You can't simply adjust the UVs as then you will start seeing sprites around your chosen sprite instead of tiling it. This is why I said you can't tile sprites. Tiled Sprite works by creating geometry rather than changing UVs.
That said, you can still create a version of a tiled sprite that will take an offset and start creating geometry in a specific fashion.