They shouldn’t! You shouldn’t even be able to feel your tampon inside you, no matter what position you are in. I suspect your tampon isn’t inserted deep enough and that’s why you are feeling it when you sit down. Make sure you put the applicator deep enough in your vagina that your fingers on the plunger are touching the opening to your vagina and then hold the applicator in place so it doesn’t slip down while you plunge the tampon up higher in your vagina. Sometimes tampons are inserted properly but slip down because they aren’t the right size. If you are a larger woman, try a more absorbent tampon and see if it will stay up inside better.
I can only speculate that it could be you are not used to inserting a tampon and/or you are using one that is too big. Whatever is causing your pain, you can do something about it. My suggestion would be try going down a size, and see what health expert Dr. Molly has to say about inserting tampons properly.
Tampons should definitely not hurt when you sit down. What I’m thinking is you didn’t insert it properly. I know it can be a little tricky at first, but it will get easier and soon enough, you’ll be a pro. My best advice is to make sure you check out this video (http://ubykotex.com/real_answers/education/article?id=50740) that demonstrates how to properly insert a tampon. I’ve had my period for years and yet I still took some good advice away from it!