Duplicated blueprints don't work like the original timeline animation on key input

I have a blueprint object that I animate on key input, using timelines.
If I copy this object in the editor and paste a few copies around, when I play the game, only the original works as expected (timeline animates on key input), the others don’t animate. What am I doing wrong?

You can see the bottom right object animating, but the rest stay put…

And the blueprint animation: