Cyndis
I think you have to download the game, even if it is on a disc, and i day one patch if i'm correct. Once you have those out of the way i'm pretty sure you won't need an internet connection to play.
You don't need an internet connection at all to install the disks to either console as far as I know. (I only have XboxOne) and you most definitely do not need an internet connection to play. Day one patch is pretty much optional.
Not sure about Ps4, but I've never seen it happen on my Xbox. Should be the same.