Hi gentib,
Thanks a for the project file!
To have the simplest setup possible, I would bake the animation and then offset the animation.
Shift C to get the Commander> Cappucino
or
Main Menu> Animation> Cappucino
Start Realtime while on frame zero. Position and Rotation are on.
Click and hold (do not move) the mouse over the object axis.
Then deactivate the Align To Spline.
In the Cloner, the Object> Reset Coordinates is off.
Instant Mode is on Instance.
Use a Step Effector, Switch scale off, and use the
Parameter> Other> Time Offset
Example
https://www.amazon.com/clouddrive/share/ErZhYr2ZUlCucIoF9Ipk8CMgzzxYzwdQqDlU4j3gfha
All the best