Titer testing is not always a good indicator of protection. See this for more info: Antibody Titer Testing as a Guide for Vaccination in Dogs and Cats | The SkeptVet
How old was Jax when you adopted him? If he was over a year old, most places I know of don't revaccinate for 3 years. My state requires rabies every 3 years (with a vaccine labeled as 3-year), and other things can be more flexible. Distemper/Parvo is important. The author of the link above recommends every 5 years once the dog is an adult. If Jax goes to a groomer, daycare, kennel, etc. they may have their own requirements. If had had a bad reaction with vaccines in the shelter, I would assume they would note that. I wouldn't worry about keeping him on a legal and reasonable vaccine schedule. People who don't vaccinate at all, ever, simply do not care about science and are buying into superstition.