Cats -- and especially cats used to being outdoors -- can get collars caught on shrubbery. They are pretty good and learning to escape! If the collar has the safety breakaway snap, it is pretty easy, too. But I don't think flea collars have that type of catch.

So you may be "barking" up the wrong tree re the neighbor.

I liked the idea of bringing them all IN, and even the idea of using a spot on rather than a collar. Flea collars are not very effective.

If you can handle the cats to put on a collar, you should be able to manage the topical stuff. It does cost a bit more.

And as someone pointed out, products are labeled DOG, CAT, DOG AND PUPPIES, CAT AND KITTENS, DOG CAT PUPPY AND KITTEN. Make sure you use the right ones.