I think the answer is in the first verse: "Old Mr. Johnson had.... a yellow cat that wouldn't leave his home." The cat came back because he wouldn't leave his home! I've read several accounts of families moving with their cat, where the cat will leave the new digs – and his human "servants" – to return to his old home, his familiar territory that he's staked out already. I sincerely doubt that Mr. Johnson's presence had anything at all to do with the cat coming back.