Hardibacker is a CBU . The hardibacker does not have the fiberglass mesh that is found in some of the others but they serve the same purpose.
I use the Hardibacker CBU routinely with no problems.
You should have no problems with the Hardibacker your contractor is using as long as it is installed per Mfgr instructions.
make sure thinset is used between the CBU and the subfloor , nails are placed per spec, and the joints are taped and mudded.
Good..Fast..Cheap. Pick any 2...can't have all three