man. I don't think this is a good idea to push an UIViewController to UISplitViewController. if you must to do it like this. you can use this method:
SplitViewController *splitViewController = [[SplitViewController alloc] init];
[self.view.window setRootViewController:splitViewController];
but, I think this is not a perfect solution. Especially, when you need to add some custom animation during push between different ViewController. thus, maybe you should custom a splitView and added it to an UIViewController. there are many sample code in github for custom UISplitViewController.
https://github.com/Alterplay/APSplitViewController
https://github.com/palaniraja/cUISplitViewController
I hope this help for you.