Basically Newt's past isn't all sunshine and rainbows. His parents were distant at best, he and Theseus were never really that close thanks to the age gap, and he'd never had any friends at Hogwarts. His whole life, the only physical affection he's received is from his creatures. Until he meets Graves.
Graves, who takes every opportunity to hug him, or put his hand on his shoulder for a little longer than strictly necessary, or just touch him with more affection than anyone ever has. And Newt loves it. He melts into his touch like a cat and practically purrs.