Facebook App is either showing me online or offline, not "available on mobile device"

Hi!

I've been looking all over the internet but nothing seems to help fix this problem.

I've always used the official Facebook app and Facebook Messenger app and just recently I discovered that it makes me appear as "online" all the time. Even when the apps are not running.
I'd have to shut my phone down or don't allow Wifi but what's the point of having a smartphone then?

Now I tried to uninstall these apps and use an alternative one, but still the same problem.

Friends of mine use the same apps, have the same iPhone and they do appear in the chat with the mobile device icon and the time it has been since they used it.

So, my question is if any one of you could help me out, 'cause this is really annoying me :)

thanks!
Sarah