If you've already ensured that the DLC aren't in your library and just uninstalled, then this could be the result of Family Share license conflict.
To resolve this issue:
1. The user that doesn't own the DLC needs to remove you from family share in their Steam profile on your PC as well as theirs.
2. Completely reinstall the entire game (verifying files in Steam won't be enough)
3. Once the game is launched the first DLC missions will immediately trigger, assuming that you're already far enough in the game. (Chapter 7 for Foundation, completed the game for AWE)