"But if the negatives are red the prints should be cyan. Right? From the sound of it both the negatives and the prints have the same colour cast. Shouldn't they have opposing colours?"
There are two things going on here: the negatives look red (actually orange) because of the film base is orange (this is normal) and the prints look red because putting them in backwards and shooting through the base is the same as shooting through an orange filter - you would not expect to get a cyan cast in teh print with an orange filter (granted, it would look cyan on the neg, but the film base's strong orange colour will overpower it visually).
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