If your phone can get a signal from a Vodafone mast then it's connected to the internet. Unless 'Data' is switched off then the various apps on your phone will keep using the internet for updates.
Each manufacturer tweaks the Android operating system to their own requirements, so what I see on my Alcatel phone might not match what you see on your Samsung one. However looking at the user manual for your phone (and then comparing it with what I see on my own phone) suggests that you need to do the following:
1. Tap the Apps Screen icon (9 dots, bottom right).
2. Tap 'Settings'.
3. Tap 'Data Usage'
4. Tap 'Mobile' (I need to do that on my phone but I can't see it mentioned in the user manual for your one, so you might need to skip that bit).
5. Tap 'Mobile Data'.
6. When you see "Turn off mobile data?", click on 'OK'.
On my phone there's an alternative (and simpler) method of doing things. So, if the above method doesn't work, you can see if the following helps you:
1. Drag down from the top of the screen.
2. Then repeat that action.
3. That takes me to a screen where 'Data connection' is shown 'lit up' (showing that it's 'on'). Simply tapping on it turns it grey (meaning that it's 'off').