Object rotate moving empty, but not when animated following empty

When moving the empty by hand, the parented objects will rotate, as specified with a driver. But when the empty follows the curve with an animation, they don’t rotate.

I had this working before in another file, but I can’t figure it out why it doesn’t work out this time.

See the short video explaining the problem: https://www.youtube.com/watch?v=ezTQR7-HLEc