Several things are happening in that scene:
First, Michael had always acted as his own consigliere. He needed Tom after the Tahoe shooting. Now, he's putting Tom back in his place.
Second, he's acting on his dissatisfaction with Tom's performance. He left the family in Tom's hands before he departed for Miami, New York and Havana. When he came back, he found that Kay had had an abortion, and the Senate committee had nearly trapped him into perjury convictions because Tom failed to discover that Pentangeli was alive. You and I might not blame Tom for these things, but I think Michael's view was that "it happened on Tom's watch."
Third, Neri was making a move to displace Tom as Michael's number-two guy. Notice the smirk on Neri's face when Michael makes that speech about the job offer and Tom's mistress--it's clear that Neri was the source of that info.