hair color correction

In case the color isn't the correct shade, it will fade, you can redye with a shade that matches the ends. 

Once you dye hair with permanent color, the underlying pigment of the natural hair color has been lifted and a dye has been deposited into the hair shaft--which reflects light and appears a certain color (reddish blondish in your case). 

To fix a brassy color, all you need to do is redye the hair without lifting the underlying pigment--besides color will not lift color because dyeing hair is very similar to painting with water colors.  For example, paint a black spot with water color and let it dry.  Simply painting over the black dot with yellow will not change the underlying black spot to yellow--it will be some color combination of black and yellow though. 

Demi or a semi dyes coat the hair shaft and have no peroxide or low peroxide, which means no or little lift of the natural underlying pigment.  These particular dyes were created to be less damaging to the hair than redying with a permanent color can be. 

Anyway, you can strand test a darker shade of brown on the roots to see what will happen, but realize that even rinsing out the roots will deposit color onto the ends of your hair. 

I hope this answers your question and that it helps.  Good luck!

I think what happened to your roots is called "hot roots".  The heat from your scalp speeds up the process and often makes the hair lighter. 

You could try using a darker color to "tone" the roots, but I'd recommend using a semi or a demi rather than a permanent color.  If you have reddish then use an  ash--only on the roots--and PLEASE strand test prior to doing the entire root area. 

Good luck!