I was under my parent's health insurance, then got my own, will I still have to owe for those months?

I was under my parents health insurance until i graduated from undergrad in May. In August, I started working full time and got my own health insurance. I am independent now... so I listed Aug-Dec for when I had my health insurance. When my parents file and claim me for the months I was still in school, will I still have to owe for Jan-May?