So what does Tessio mean when he says "tell Mikey it was only business. I always liked him?"
Tessio made a mistake in judgement. He had no personal animus towards Michael.
From Tessio's (limited) POV it appeared that Michael was requiring Tessio to take a dangerously weak position towards Barzini's incursions-a position that could only end with Tessio eliminated by Barzini, Tessio forced to accomodate and submit to Barzini or Tessio hounded out of the business completely by Barzini. Tessio made a business decision that now was the right time to jump ship to a "winning team" but it wasn't because he was jealous of Michael or disliked Michael... although he would have overseen his murder...
