In theory css parallax is brilliant and should replace all bloated js versions. In practice, it's unusable. We spent 40 hours as two experienced frontend engineers trying to get the example to work on a relatively simple example but it requires such a specific markup that it became too convoluted. Eventually I gave in and looked for a js solution but those were much larger and slower than we wanted. Ultimately, ended up writing a short 100-line open source vanilla js lib, and a bunch of folks seemed to be having our same issues: https://github.com/dixonandmoe/rellax. That said I still love to explore the extents of css' capabilities but this is one time where it fell short.
Exact same problem, actually tried making this example mentioned here to work on other browsers besides Chrome and failed to do so.
Your rellax library looks really useful i just hope i won't have to build parallax websites anymore.