My question involves a background check in the State of: Florida

I was convicted in NY and served 1 yr for each charge of endangering the welfare and attempted burglary. I stayed in Nassau county jail for each yr. I now currently live in Fl and when asked on applications if i have ever been convicted of a felony, I put No and take the chance when the background check is run.
My question is this, why is it that my felony shows up sometimes and other times it doesnt when i apply to jobs.
Was it because I didnt do state time?
Will it show up on a 10 yr background check?