Spotting white worms around the cat are likely tapeworm segments.
Cats that are hunters are very likely to pick up worms from their prey.
Recommendations are to worm dogs and cats every 3 months, the roundworm eggs, even when poo is picked up by diligent owners can be left in the grass, and if picked up and ingested, particularly by children or immunocompromised people can cause blindness.
Most cats and dogs will not suffer from the worms, including tapeworms, but the spread to people is the concern.
I have three prolific hunters here, and was spotting tapeworm segments coming out 3 months to the day from the last worming last year, so I have changed to worming my cats every 2 months.
We do not seem to see the same problems with wormer resistance in cats and dogs yet as we do in farm animals, so the recommendations to protect children in particular, I firmly believe in.
Hope that helps
Suzanne