I am still not very experienced in the spline modeler so forgive me in case I ask something obvious.

I am interested in this topic too and I was able to create some animated spline objects, that
are close to a "growing vine". But the only method I found was to animate the points of the spline with moving the around to simulate the grow effect.

Is there another method in Carrara I haven't found yet to extrude the object along the spline which is more like the percentage based extrusion mentioned in the tutorial?