Well, that's the great thing about the Trilogy: the films are so rich in detail that you can always spot a new and interesting nuance no matter how many times you've seen them.
I'd guess that FFC put Neri behind Michael in that scene to emphasize that he's the new Don (and thus merits bodyguard protection)--just as he emphasized Vito's retirement by having him dressed like an old Sicilian peasant and peering into his fishtank all the time. In the novel, Neri doesn't become glued to Michael until the period of time between Tessio's proposal to meet with Barzini "on my territory--where you'll be safe" and the Great Massacre of 1955.