Netflix download movies and shows when you are not actively using the app , but its success depends on your device’s settings and the specific feature you are using.
While the app supports background activity, mobile operating systems (like iOS and Android) often limit how long an app can stay "awake" once it's closed or the screen is locked to save battery. Background Downloading by Feature does netflix download when you're not on the app
Netflix uses different systems for background downloads, and they behave differently: Netflix download movies and shows when you are