Once a repair has been completed, can I replace the tile right away?
Upon completion of a repair it is completely safe to apply thinset and tile. Just make sure your ohms readings are correct before tiling. Typically you would use a flat trowel to apply some thinset over the cable and then back-butter the tile and fit it in place. To ensure none of the moisture in the thinset ruins the repair, a liquid adhesive can be applied to the splice and heatshrink as added moisture insulation.
Do not turn on your system until the thinset has fully cured.