If I understand correctly, the input curve is animated, and you're trying to use both the curve from the current frame and the initial frame.
The issue is that whenever an asset is evaluated through Houdini Engine, The Houdini world only gets a snap shot of the host application world. So from the Houdini side, the mesh would appear static. So the asset only has access to geometry from the current frame. Unfortunately, this is a currently limitation of Houdini Engine.

Maybe a workaround is to have a second input for the initial curve?