Hi Mrs P.
Yes dead worms will come out one way or another - looks like the rescue did a good job.
Cats need to be wormed every 3-4 months if they go out at all, less if they remain indoors.
People may occasionally pick up worms from animals, but transferrence directly from cats to humans is uncommon but not impossible. Your pharmacist can advise you on medication if you suspect you have a parasitic infection.
Pinworm is common in children. Tapeworm is transferred by the accidental digestion of fleas.
Those wiley Australians have done a good article - scroll down to the bottom, there's the information you want at the bottom.
http://www.cat-world.com.au/internal-parasites-in-catsDon't worry, treatment for fleas and worms becomes routine after a while.