The only thing that Saito promised at first, was that he would have no problem getting through immigration. That, he could fix with a single phone call. The rest of the job would take some time and influence, of course, to help clear Cobb's name, but the only thing that it was important to actually see happen in the movie was for him to get through customs.
The fact that he was allowed to talk to his children on the plane implies that the kids' grandmother doesn't believe he killed his wife. So he is ok to be there to see his children. No one from home is going to turn him in. Saito, then, would be working on clearing his name. How he was going to do that, we don't really know. But he said that he could.