I know this is just a movie and anything can happen just because the writers write it that way But.....

In some ways Michael and Vito forced Tessio/ or Clemenza to jump ship. Why you ask, well, if they would have kept them in the loop and explained their plans to whack the crap out of everyone once their guard was down then they would have stayed loyal worked hard and played along knowing that they would have been taken care of and not left behind. They were almost forced to try something to stay on top for what they saw around them going on.
You have to wonder why Vito would not keep his long time friends/ partners and capos up to speed. At this point there was no reason to not trust his two long time key people. They spent many years together and went thru all kinds of good and bad times. It was Michael and Vito's decisions to keep them shut out that causes Tessio to look elsewhere.

Before you speak of the possible problem of turncoats if to many know the plan, what makes you think that someone in the newly built regime wouldn't have sold out the plan to get ahead with the family rivals. These were fairly new to the family when you think of how long Tessio and Clemanza were with the family. After all like Michael tells Tom, they are all business people.

You kind of have to wonder who's idea, Michael or Vito- it was to cut the two old Capos out? Maybe they were so worried about someone that their own actions drove it to happen.