I don't think the owner is on the hook if they simply use the service. The individual wasn't the one who truly decided the essential means and purposes beyond personal use, Meta is the one who did that and is thus the controller for that processing.

And I believe in case of European users the contract is between Meta Ireland and user, Meta Ireland is the one who would be the one doing the exporting in that case.

Now if user actually did publish it on Meta's service for broader consumption then they might become controller for that & if initial purpose was that then the initial recording is unlikely to be exempted under household exemption.