Salon color dramatically lightened within 2 weeks

I have been a redhead all of my life (Strawberry Blonde being my natural hair color). I decided to go to the "dark side" and become a brunette. It works well with my very fair skin and blue eyes. My colorist used Surface 5N and 5NB and kicked out most of the leftover red with Keune (green?). I know it's a process.

Before I saw her, I colored at home with Wella Color Charm (boy do I loathe that product) 8RG, 7R, and 8G. The result from my salon color was almost a 3N look, which I did like and it suited my skin and eyes. The only thing is is that it was one dimensional. 3 Weeks later, boy are those gold tones coming back and now my hair probably at a level 5.

I don't want any warmth in my hair, as I'm a very fair, cool pink undertone, woman, and dark really does work on me, as long as it is cool toned. I am assuming my colorist will have to kick out the gold tones by adding a red toner. Is that correct? I also want to add dimension to the dark brunette, but I am not sure what level to go with to add dimension? I know I can go lighter by 2 to 3 shades as a highlight, but I don't think I can go any darker.

Can all of this be done in one salon session?

Thanks so much in advance!

(That was a lot, I know)