Disclosure of academic dishonesty during background check for tenure track
The purpose of the background check is to find out if you are likely to abuse children on campus, assault your colleagues, or steal from the university.  It is not related to academic integrity.  

Academic integrity is evaluated by reference checks and transcript checks.  

Convictions are decided by law courts, not university committees.  You have a conviction if a judge or jury convicted you in a court.  This does not include university honor courts that are not part of the legal system.


  So how should I report this incident with my prospect employers?


You should report it if you are asked to do so.  You probably will not be.