White won't be coaching RB's next season. Unfortunately, the guy who may get pushed out in this move could be Perkins (who has done some nice recruiting and did some decent DB coaching under RE).
I'm guessing that the reason coach Brown took over the corners is because he prefers a rechnique different from what Perkins taught (it is open for debate which is better) and because of this I think Perkins will be on the chopping block (in favor of White, who has coached both DB's and LB's in the past). I personally would prefer White get moved to LB's (and in a perfect world, Richardson return as RB coach) but this is a pipe dream.