"Usage does count if while the phone is off if you left any apps running in the background. Double click the home button and anything that shows up in the bar is still running whether the screen is off or not. Hold any of the icons down until they wiggle and then close them out.
This is only true if the app is truly multitasking, like Pandora or GPS running in the background. For everything else, usage is not accumulated. Looks like you skipped that day at Apple Tech school.