I have read something in the past about a "leuco cyan" problem. It occurs in color negatives processed with bad chemistry and it has not to do with the film; the dye that should come out cyan comes out colorless instead.
Having no cyan in your negatives, it makes sense that you don't have any red in the prints.
Try searching for this leuco cyan thing. It is said that it is possible to correct, in case you have important negatives.