Dyeing over red hair

New growth shouldn't have come out uneven, unless she didn't apply the dye evenly or thick enough.  If you mean it just looks uneven with the old dye, that is common.  Using dark colors on lighter hair can cause the base color to show through instead of the dye coming true.  It will probably fade more and more purple as time goes on.  Since it was a dark dye, she will either need to keep it dark if she's going to dye it again, or use a color remover to remove the dark dye before dyeing it again, because she won't be able to lift it with dye. 

Typically when one wants to go from lighter hair that has been dyed before (is porous) to darker, applying a protein filler first helps.  You also need to choose a dark dye with a base color that will counter whatever color your hair is (if her hair was red, she should have used a brown dye with a green base).  If you're there helping her, be sure she test strands everything she does from now on.  Her hair is pretty porous now from all that dyeing and she can expect the porous stuff and new growth to react to any dyes different ways.  Doing a test strand will warn you of what you're about to do!