Hi background-permit,
Since I wrote in a forum, I have to explain it on that level, not an evaluation of anyone's knowledge.
Ani polygon object has an axis; this Axis is the "sub-world" for the points.
Points are typically not connected to the World space, and it would have many problems if they were.
If an object is only moved by Axis, the information of the points (e.g., position) stays the same.
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To work around this, you need a copy of that object and have it not moved. You can place its Axis to the World Axis, but it can be anywhere, as long as it is not moving, while the target is purely moving points. This is how I understand your target. Now, the object that moves in a hierarchy moves the object and the points. This new position can be transferred to a static copy of that exact mesh.
Now, the Axis stays, but the points are moving. This new object can now be cached or used for PLA (Point Level Animation).
After caching, switch the XPresso off.
Example
Please note that I do not have your file here, and any answer might be flawed, as nothing beats a project file in a forum-based communication.
All the best