New iOS 13 Modal Presentation: Presenting Controller Doesn't Move Down

Turns out the problem was my view controller hierarchy. I was able to fix it by making the presenting view controller the root view controller of my app. First I set the background controller as the root view controller by calling

window.rootViewController = self

and then using my previous code

let controller = storyboard?.instantiateViewController(withIdentifier: "tutorial") as! TutorialController
controller.modalPresentationStyle = .pageSheet
controller.modalTransitionStyle = .coverVertical
present(controller, animated: true, completion: nil)

I presented the view controller. Thanks to everyone who tried to help!