The behavior the author described has been called 'milk treading', and is thought to be originally the way that kittens coax milk out of their mother cats, but

The behavior the author described has been called 'milk treading', and is thought to be originally the way that kittens coax milk out of their mother cats, but later in life can be a regression to a trusting kitten-mother like relationship between a human and a cat who trusts that human. If your cat milk-treads you, your cat likes and trusts you, at some level, at some times.