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How is it updating on it's own? As in how can you tell?
 
Using my 5S this morning and the app icon for Facebook was showing it being downloaded/updating.
The little blue dot you mean? From what I recall that sometimes can be the case when there's new data in the app not necessarily an app being updated. In my case the opposite usually happens where I update the Facebook app actually but pretty much never see the blue dot next to the icon.
 
That's an update of the app from App Store, you have to turn off updates under iTunes & App Store I settings if you don't want what.
What you have turned off is updates in the app so it's updates your feed when you open Facebook app and not in the background.
 
No dot...it looked like a pie chart overlaid on the icon and as the dial filled up, the app was updating.
Ah, I misunderstood, so it was actually updating as you were watching it happen. Interesting and certainly odd in that case...unless you don't have app updates disabled (as I thought you implied you had, but reading the OP again it seems like you actually didn't).
 
The little blue dot you mean? From what I recall that sometimes can be the case when there's new data in the app not necessarily an app being updated. In my case the opposite usually happens where I update the Facebook app actually but pretty much never see the blue dot next to the icon.

I have noticed that when I update an app over the air on the phone itself, then it shows the blue dot. If updated through itunes, there is no blue dot.
 
I have noticed that when I update an app over the air on the phone itself, then it shows the blue dot. If updated through itunes, there is no blue dot.
I've had experience mostly over the air and while usually there is a dot sometimes there isn't one for some reason with some apps, especially Facebook.
 
I've had experience mostly over the air and while usually there is a dot sometimes there isn't one for some reason with some apps, especially Facebook.

Yeah I had the same experience with the last Facebook update.
 
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