Hi OPS,
The Display Tags define, to a certain degree, the appearance of the Object. It does not alter the Geometry. The Geometry is the part that the Volume Object takes from the Object. Similarly, it wouldn't matter if the Object has a metal or glass material for the Volume Object.
Please try the Advanced Tab of the Volume Material for that. An example is below with animated values over the whole time.
Is that working for your project? If not, please share a simplified example as a C4D file here. Thank you.
Enjoy your Sunday