Revealing parts of a volumetric shader using dynamic paint

I have a torus that has a procedural shader that mixes a transparent shader with an emission shader factored via a dynamic paint image sequence to have the torus appear from nowhere in a reveal.

I am trying to have the same reveal animation effect using the material volume output; also driven by the dynamic paint.

But the dynamic paint does not seem to affect the volumes shaders. I presume this something to do with volumetric data being 3D.
I was wondering if anyone has an idea how I can have the same reveal effect for the surface and the volume output ?