When asked to turn off smart lights, set alarm or any other command, video pauses on Fire Cube.
That may be by design, since audio on the Echo units pauses during a command (at least on the content I've listened to), so that nothing is missed. If the video resumes without requiring additional effort, it seems like the type of behavior most people would desire. If it stays paused, however, that would be a clear design flaw. (I have multiple Echo units, but don't have a Cube).