Clone animation via expression to other layers

Hi,
I'm not 100% sure what you're trying to achieve. I think you're trying to copy postition parameters to other layers but with a time offset, right?

If yes, you can use the expression 

valueAtTime()

1. Create your animation on your target layer.

2. Create the child layer.

3. Create the following expression on the xPosition of the child layer:

thisComp.layer("target").transform.xPosition.valueAtTime(time - 1)

Now those layers take the xPosition of the layer "target" with a time offset of "time-1" = the actual time - 1 second = 1s offset.

If you have multiple layers that should all have a time offset of 1s of the layer below you can write the following expression:

thisComp.layer(index+1).transform.xPosition.valueAtTime(time - 1)

Now the child layer takes the layer below (index+1) and then you can create unfinite layers with the same expressions.

Did that solve your problem?