The "Link Timeline" feature is a feature accessible in the Composition Tree and is related to Timeline Animations. Control Applications only play out Timeline Animations of Subcompositions at the Root level of the Composition Tree structure. That being said, you can force Control Apps to run the Timeline Animations of nested Subcompositions by "Linking Timelines."
Activating the "Link Timeline" Feature
To play the animation timelines of a nested Subcomposition (a Subcomposition nested beneath another Subcomposition), right click on the nested Subcomposition in the Composition Tree and select "Link Timeline". When the Timeline Animation has been successfully linked, it will turn green in the Composition Tree.
You will also see the Subcompositions with Linked Timelines show or hide when toggling the Linked Timelines button (chainlink icon) in the top left of the Composition Navigator.