http://www.latimes.com/local/lanow/la-me-golden-state-dna-match-20180427-story.html
They took DNA from the crime scene and matched some portions to DNA relatives had submitted to GEDMatch. Doing this they traced back to his ggggrandfather. Genealogists then traced the line that moved to California and found likely people to check out. They then took his discarded DNA from the trash and matched it to the crime scene DNA.
I don’t see any invasion of privacy. If he were smarter, he would have handled his trash in some other way like hauling it himself to a dump site to be mixed in with thousands of others. I heard some speculation that he may have stopped his crime spree when DNA evidence began becoming more in use in police work. Being a former cop, he would have known this and it may have induced him to stop for fear of being caught.