You just need to add the transition to the window's layer, and present your controller rather than pushing it:
CATransition* transition = [CATransition animation];
transition.duration = 1;
transition.type = kCATransitionFade;
transition.subtype = kCATransitionFromBottom;
[self.view.window.layer addAnimation:transition forKey:kCATransition];
[self presentViewController:adjustViewController animated:NO completion:nil];