When I have made perforated plastic ornaments I have used a second piece of perforated plastic to cover the back. The two pieces are stitched together using a running stitch, or a double running stitch. Sometimes I leave the back blank and sometimes I have something stitched on the back.
Below is a close up photo of the back of one of my perforated plastic ornaments. As you can see I stitched the main part of the ornament together using white thread. I stitched the heart using the gold metallic thread. (Neither is that obvious to the naked eye at actual size.)
If the design has back stitching one could do it, or some of it, through two layers of perforated plastic. A double running stitch would make both sides look they had back stitching.