Apps and streaming devices (Roku) both get programs from the Internet, so each is steaming. The only un-metered data are TV networks via Contour.
If you don't stream a lot, you may be leaving the Internet streams to continue in the background while watching...or not watching...TV. I always exit Roku via its Home Page or terminate any streaming program before closing it.
Cox doesn't charge to use streaming apps. Cox only charges if you exceed your data cap of 1.25 terabytes.