Hello and thank you for using this site to help you. I am sorry your question was not picked up sooner.
If he only ate the plastic applicator and not the actual tampon, chances are he chewed it well enough to pass. But in case there are any large pieces you will need to watch for a blockage of the intestines. Symptoms of this are sudden lack of appetite, vomiting, diarrhea and lethargy.
For now I would do a wait and see if he passes it out in the stool. I would also give him a tablespoon of pure canned pumpkin now so that it cushions any sharp edges of the plastic and carries it through the system safely. I would also give a tablespoon of the pumpkin each day for about a week.