Cutdown Hair Colour. You should cut down the processing time. Do 2 dye sessions to avoid over-processing your hair.
By putting a toner with the opposite color in your hair you can really tone down and neutralize the brassiness or red tones. Using a cool or ash-toned hair color will help balance out the red tones and give you a more accurate hair color. Some hair is more resistant to color than others.
Lower the temperature on your hot tools to prevent damage and always apply a heat protectant all over strands prior.
These kinds of shampoos help to deposit that back in the hair in order to nurse it back to good health. To keep the color reapply a few times per month or more. For hair that is too brassy use purple or blue toning shampoo. All hair is different and may take longer to soak up color or maybe no time at all.