Can I own a gun if my felony in California was reduced to a misdemeanor then dismissed?

I have an opportunity to work at a prison in Texas. Two of the requirements are that I have no felony's and can legally posses a gun. I hired some lawyers in California and they discovered that my 2 felony's (for fistfights) from 1979 and 1980 had been reduced automatically to misdemeanors based on the original plea agreement (I think 1203). So I employed them to have the cases dismissed, which they did. I found out from the federal government background check that I cannot own or possess a gun. What’s up with that? The cases are dismissed. The judges let me enter a retroactive plea of not guilty and dismissed the cases. I am not a gun nut and don't care to own one but I would like to work at the prison! HELP! Please!