It says that anyway if you restart the program and it finds a part you already have.
Don't panic!
I had quite a few fluffs when I was getting used to Jdownloader and now I use it all the time to get edits.
I had to use it a lot about a year ago, I lost my whole collection when my hard drive decided to go tatty bye-byes on me.
It's a really, really good program once you get used to it.