Content not refreshing in iOS apps
You are confusing between two different features available in iOS.

What you are observing is the iOS default behaviour and is called state restoration. As long as an iOS device has available memory (main memory or RAM), it preserves the running state of most recently used app(s). The assumption is that the user is likely to re-open the recently used app.

Background app refresh setting is relevant for apps that need to communicate with remote sever over the Internet to fetch data (typical example of such apps is social networking, email client apps etc.). Enabling background app refresh for an app (if enabled), will let iOS fetch data for such app at opportunate moments (such as when iOS device data connection is activated). This enables the apps to instantly present up-to-date data to users when launched, thereby providing a good user experience.

Since invoking device radio costs a relatively higher battery usage penalty, enabling this setting ensures best user experience while optimising resource usage.