Hi Scott,
Your findings are correct, the volume is generated based on the DSM and not on the mesh.
It is not possible to overlay more volumes of the same area in Pix4Dmapper. You could compare the volume changes over time by using the exact same base surface. As Aaron mentioned, I would create the base surface in a Pix4Dmapper project, export it as shapefile and then import it in the other Pix4Dmapper project. However, it is a bit cumbersome to compare volumes over time using Pix4Dmapper alone.
This tool might be more suitable for your intentions (due to its timeline functionality): Compare stockpile volumes over time.
An alternative would be to export both the DTM/DSM files from each survey over into another software that is able to compare the two DTM/DSM datasets such as Global Mapper. More info can be found in this community post: Cut and fill software.
Best,
Teodora