Do I still need proof of vaccinations if I'm traveling with a cat?
According to the USDA, you do. In addition to inoculation against rabies and distemper, cats entering Mexico should also be vaccinated for panleukopenia, rhinotracheitis, and calicivirus.
You will need to carry an International Certificate of Good Health plus proof of these vaccinations (and proof of ownership) for entrance into Mexico and re-entry to the US with a cat.