Mosasaur image by Dmitry Bogdanov - firstname.lastname@example.org
Hypocercal means that the vertebrae extend into the lower lobe of the tail, making it longer. As near as I can tell modern fish don’t have hypocercal tails, but some early fish had them.
K. A. Kermack made a 3-D model of an early vertebrate that had a hypocercal tail in 1943, and put it in a wind tunnel to see how the tail affected body orientation. Kermack’s conclusion was that a hypocercal tail causes pitch-up tendencies, at least in the Pteraspis ostracoderm.
Why did these three groups of marine diapsids evolve hypocercal tails? They’re not particularly closely related. Thalattosuchians are archosaurs, crocodylomorphs. Mosasaurs are derived lizards. Ichthyosaurs origins are still argued about, but they’re not archosaurs or squamates. There had to be a physical reason.