Hi Khanh Ha,
I've tried applying various CSG operations and I don't get any surfacing errors, the tools::volumeToMesh output is always a closed manifold surface, no holes.
I was actually not able to exactly reproduce your last image from the setup you described and I also noticed that you are mixing different voxel sizes, the CSG tools require grids with matching transforms.
This is what I get using your setup for the sphere { radius 100, center (1.5, 2, 3), voxel size 0.5 half-width 3 }, no neutering. (The sphere grid is re-sampled to match the Armadillo model's transform, voxel size 0.1 .)

But let's move the sphere away from the Armadillo man's crotch to { radius 50, center (0, 100, -30), voxel size 0.1 half-width 3 }, this generates the following result:

The mesh output seems fine, I strongly suspect that you are experiencing a visualization error and not a mesh extraction bug. I can't really debug this much further we don't have access to Windows and VisualStudio.
What version of OpenVDB are you using? The latest version is 3.1
Best,
Mihai