Actually it is 100% opposite of what you said. From your link a breakthrough case is defined as a case 14 or more days after your last dose. Not defending or refuting the effectiveness of the vaccine, but misreading the link can cause issues.
For the purpose of this surveillance, a vaccine breakthrough infection is defined as the detection of SARS-CoV-2 RNA or antigen in a respiratory specimen collected from a person ≥14 days after they have completed all recommended doses of a U.S. Food and Drug Administration (FDA)-authorized COVID-19 vaccine.
