Looks like there are no direct way to do this to detect if user has tapped on home + power button. As per this, it was possible earlier by using darwin notification, but it doesn't work any more. Since snapchat is already doing it, my guess is that they are checking the iPhone photo album to detect if there is a new picture got added in between this 10 seconds, and in someway they are comparing with the current image displayed. May be some image processing is done for this comparison. Just a thought, probably you can try to expand this to make it work. Check this for more details.
Edit:
Looks like they might be detecting the UITouch cancel event(Screen capture cancels touches) and showing this error message to the user as per this blog: How to detect screenshots on iOS (like SnapChat)
In that case you can use – touchesCancelled:withEvent: method to sense the UITouch cancellation to detect this. You can remove the image in this delegate method and show an appropriate alert to the user.
- (void)touchesCancelled:(NSSet *)touches withEvent:(UIEvent *)event
{
[super touchesCancelled:touches withEvent:event];
NSLog(@"Touches cancelled");
[self.imageView removeFromSuperView]; //and show an alert to the user
}