When painting Vertex Colors, you are only painting on an individual Instance of the material and not the actual material asset itself.
If you want to apply the vertex color data to another instance of the mesh, you can copy and paste the data onto another mesh or multiple meshes.
When painting vertex colors, the Instance Vertex Colors field will display information about the selected mesh(es).
This displays the number of bytes of memory used by the vertex color data (stored in the map package.) This value reflects the total for all assets that are currently selected.
Copies the instance vertex color data for the selected mesh. See Sharing Instance Color Data for more information.
Pastes instance vertex color data that was previously copied. See Sharing Instance Color Data for more information.
Discard the data for all selected meshes and restores the default vertex colors.
Attempts to match stored instance data on re-imported meshes with different vertex counts. See Vertex Color Matching for more information.