This photo made me laugh. I was thinking how there is no way I could get one of my cats to walk on a leash, never mind with a dog. I'm impressed by this lady.
My own cats have reacted to the new dog in their own ways. The bigger cat, the boy, ran away and hides whenever he sees the dog. He's a big chicken anyway. The smaller girl has made the dog understand that this is her house and must follow her rules. The puppy now avoids anywhere that cat is. The cat makes that difficult for her by sitting in doorways and staring. Poor pup just wants to play but the cat is having none of it! She might be half the size of the dog but she's mastered the art of intimidation.
I'm sure they'll work out their differences eventually but I'm not sure they'll ever be seen walking on leashes together.