Material stretched on generated mesh

[_Aka_]

I took a quick look at the example you mentioned. As I understand correctly, you change the material of the caps, not parts of your extrusion.

The scene do have different materials for different parts of the extrusion. Look at the Meta CG Options components on the control points of the extruded shape
https://curvyeditor.com/doclink/metacgoptions
Also, do not forget to set, if it is not done already, the corresponding options in the Shape Extrusion module, the Cross tab.
https://curvyeditor.com/documentation/generator/modules/shapeextrusion?redirect=1#cross