In print, production is the act of taking the raw inputs (copy, graphics, layout) and getting it out the door. E.g., the print production managers I know manage the physical details of the print medium. There is a similar meaning in advertising. 
Looking at the resumes of the first couple producers, one's a designer, the other lists himself as "Nerd". So I think they are using the meaning from publishing: people who produce the final product.