Tensile load capacity is pretty much the resin that keeps the fibers from moving.
The most I could find about the design
> The entire pressure vessel is comprised of two titanium hemispheres, two matching titanium interface rings, and the 142 cm (56") internal diameter, 2.4-m (100") long carbon fiber wound cylinder – the largest such device ever built for use in a manned submersible.
suggest that yeah, they relied entirely on its compressive strength of it