Can you post a specific test case? Here's my 10 minute test case and it works...
Click to view attachmentVase is a model. Action 1 is an action for Vase that uses Cylinder as an action object and moves it back an forth.;
In the chor, Action 1 has been dropped onto Vase
Sphere begins not being constrained to the action object, then is constrained to it starting at frame 20. From frame 20 onward Sphere moves with Cylinder.