As long as they are being properly dewomed, then you shouldn't worry. They'll soon be gone. And, yes, it is not unusual for you to see the worms still moving after the dog has passed them. Just be sure to clean up after them right away after they go.
You really need to know what kind of worms you are dealing with. Roundworms? Hookworms? Tapeworms? Tapeworms are caused by your dog ingesting infected fleas, so if it is a tapeworm, you need to be sure to not only get the dog dewormed (at the vet), but you need to be diligent about getting rid of the fleas, too. The other worms are present in common environmental stuff (like dirt), and you can treat them with dewormers that you can get OTC or at the vet. Some heartworm/flea medications also contain ingredients that fight the worms (except maybe not tapeworm), so you can keep most of this under control with the right once per month treatment.
It's not a big deal, you just need to treat it and stay on top of it.
BTW, you can almost guarantee that every puppy has worms and needs to be treated. One of those types -- I forget which one although I know it isn't taperworms -- lies dormant in the mamma and passes to the pups through the placenta, so they are born infected.
__________________ Life is merrier with a Yorkshire Terrier! Jezebel  & Chuy  ... RIP: Barkley  Loosie  & Sassy  |