When selecting a video with UIImagePickerController, it directly goes to a page showing the video and allowing me to play it. What event is called at the moment this page is displayed ?
It's not the didFinishPickingMediaWithInfo event because this one is called after I click on choose on this last page.
I would like to add my own controls on this page.
Using UIImagePickerController precludes you from changing the appearance of the album, as outlined by Apple here.
Important
The UIImagePickerController class supports portrait mode only. This class is intended to be used as-is and does not support subclassing. The view hierarchy for this class is private and must not be modified, with one exception. You can assign a custom view to the cameraOverlayView property and use that view to present additional information or manage the interactions between the camera interface and your code.
Emphasis mine. The exception does not apply in your case, since that is for the camera.
A solution for this then would be to create your own picker, for which there are plenty of articles and questions that outline the various items needed to do so.