I dont own a XboxOne so excuse me.....
When you get a XboxOne do you just Transfer your Current Xbox360 Gamertag to the XboxOne?
or
Do you make a New Gamertag when you get a XboxOne?
if it is the first one, then it could be possible that you transferred all your DLC to your XboxOne and now your Xbox360 thinks you do not own the SharePack/and Other DLCs that you might have
if this is the case then License Transferring your Gamertag back to the Xbox360 should fix the problem
again I am not sure that is how it even works with XboxOne, just a thought