Kittens had dewormer and just saw what I assume are deadworms in several pieces in litter box

I have never had a cat or kitten who had worms. I have three adult cats and three kittens we just took in.  The kittens went to the vet for the first time yesterday and were given dewormer. The vet did find worms in the poo ( he only checked one of the sampled I brought him) Are these dead worms a risk for my child or adult cats ? Could they still be carrying or able to transmit these worms? We let them explore the house today.

 The vet said a couple hours and the kittens should be fine for the worms.  That was 12ish yesterday afternoon. One of them threw up today once in front of my husband and once in the room they are being kept in (for now) when we werent in there.   I am not sure if it was the same kitten. I am going to call the vet first thing tomorrow. Should I be freaking out and worried about this kitten?

I hope I make sense. I am just worried for my son because he got scratched yesterday badly by one of them and my adult cats are big spoiled babies.

Thanks!

It is common for kittens and puppies to have roundworms.  Your child should not be infected if he or she does not handle animal poop.  If you keep the litter boxes in places a child cannot get to them to use them for sandboxes.  Roundworm eggs are deposited into the environment in animal feces and remains. Pets (and kids) can ingest infective eggs from a contaminated environment. The larvae released from the eggs mature to adult worms which cause infection in the host.

The litter box they are using is in their own little room and no one is playing in the box. I was more worried about cross contamination from their little paws somehow.