RE: Tracking the movement of fingers to a hand and applying that to other compositions

I would tie the position property of each Puppet Pin to a null that you could use as a paster parent for each layer or nested comp, or property you want to follow the movement of your puppet pins. You can start that by simply adding a null, pressing p to reveal the position property, then selecting your puppet pin layer and pressing U to reveal all keyframes, then pressing Shift + F4 to reveal the parent link column. You can then drag a pickwhip from the new null position property pickwhip in the Link/Parent column to the appropriate puppet pin. This will even work between nested comps if you separate the timelines in your workspace so you can see them both. No coding skills are required.

Hi,

look's like you want to use your "puppet pin position" data, to drive your other layers/comps.

The simple solution is,

Select your "layer" that have the "puppet warp effect" (in the timeline panel) and hit the "U" key twice ("UU") to revel all keyframed properties.

Select the "puppet warp" effect. select one of the points you want to get the data from (in the "viewport"), and they will get brighter in the timeline panel (look under "effects" "puppet"  "mesh(number)"  "deform").

Under the "highlighted property", you will see "position". select it and press CTRL+C to copy.

Make a new "null object". (a sort of a guide layer)(layer>new>null object).

open it's position property(press P), and press CTRL+V to paste, (make sure your playhead is on the first frame), and you got one of your points tracked.

Now, you can "parent" other layers or comps to (make them child's of ) the null. 

(repeat this how many times as needed until you have a null for each "puppet pin" point you want to track).

(you can copy or move the nulls to a different comp they will not lose their keyframes).

I hope it's helpful