I have noticed that the spinning network activity indicator doesn't always show up when I know it's using the network. For example, I have my iPhone SE and my iPad 2 both downloading iOS 9.3.2 right now. The icon shows on the iPad but not on the iPhone. And then when I start typing a question in Stack Exchange, the phone does show the network being used as it searches similar questions but when the search is done, the icon goes away even though the phone is still downloading over WiFi. Searching for tags, though, it does not show the indicator. What is the cause?
Bear in mind that the visibility of Network Activity Indicator is managed by the App's Developer and not the System detecting a connection.
That being said, there are numerous reasons for this behaviours you're experiencing. Perhaps the Apps were coded to react differently to different actions, or they wrongly hide the Network Activity Indicator despite the fact a connection is being made.