As I saw it, Neri hesitated before leaving the room because he turned back briefly to grab a smoke from the box on the table. Tom was in the room because Michael wanted to talk to him privately about Fredo's whereabouts. I guess it was too "personal' at that point to share with Rocco and Neri.
Ntra la porta tua lu sangu � sparsu, E nun me mporta si ce muoru accisu... E s'iddu muoru e vaju mparadisu Si nun ce truovo a ttia, mancu ce trasu.