It's not telling you to buy data, it's warning you that you need to free some space.
The phone won't treat the SD card as an overflow automatically: if you want something stored there you need to move it there or tell the phone to use the card. And apps always install to internal storage (Samsung added the option to partially move apps to SD back in some of their phones after it was deprecated in Android 4, but I don't offhand know whether that includes the S3). So move stuff using the file manager, check camera settings to tell it to store stuff on the removable card, etc. Then go to Settings > Apps > Downloaded (or whatever Samsung renamed that to, as they change the menu structure), select an app and see whether there is a "move to SD" button. If there is, you can move part of that app to SD (but only part, and if you use a widget provided by the app then moving it will break the widget). If the button is there but greyed out your OS supports moving but that app won't let you. If the button isn't there and it's an app you installed yourself then your OS doesn't support the option (pre-installed ones can't be moved, but live in a different space anyway).
