Who I have the same questioned this topic

When you are connected to your wifi router, you aren't using your cellular data plan. However you need to ensure that the wifi sleep policy for wifi radio on the phone is set to keep it on whenever the phone is inactive while connected to the wifi router. Otherwise the cellular data connection can become active for background syncing when the screen is turned off. The other option is to turn off the cellular data connection while you plan to be connected to the wifi router for extended periods of time.