Walt the problem is that the peroxide developer in the dye is having a lightening effect on your natural hair, and when hair lightens it goes through the range of tones all the way up to light yellow but you are stopping long before that around the rusty shades, even though your hair is naturally mid brown, the browner tones give way to the rust.
In theory it is the toners or reflects in hair dye that will counter this effect. I reckon box dyes just don't contain quite enough ash to correct this in your hair, for reasons mentioned above about people using them over highlights and going green, etc.
You might do better with a professional dye where you can pack as much ash into it to correct the ginger whilst still depositing colour.
Something like a Majirel 6.11 would be ashier than anything you could buy in a box. Green ash kills ginger. Try it with a 20 volume developer. Ebay is an easy place to buy. Here's what you do.
Majirel is 50ml tubes, and needs to be mixed with times and a half its amount. So a 50ml tube gets mixed with 75ml of 20 volume peroxide. Squeeze the tube into a non metal dish, then add the peroxide, and mix. Development time is 35 minutes, you then add water in the shower and it will sort of lather up a bit, rinse, shampoo, condition, etc.
If you are only doing roots you need less amount. I find 1 tbsp (half a tube) is a good amount, which you of course then mix with a tablespoon and a half of developer.
A strand test is a good idea if you are doing the whole lengths of your hair, to make sure its not too dark or scary and that it is worthwhile doing in terms of the tone you achieve. To do this mix a really small dab of the dye with a slightly bigger dab of peroxide (aim for the 1:1.5 ratio) , snip off a few strands of hair from an unobtrusive place in the middle of your hair, secure it with a sticky label, paint the dye on, wrap it in tinfoil, keep it somewhere warmish, 35 minutes, rinse and observe in natural light.
Capital hair and beauty is a good website for buying the stuff. Might need to say you are a student, but most supply shops will sell to the general public.