Honestly, looking at that photograph, if that is the worst it gets I would just ignore it, at least for now. The colour variation is so slight that no one is going to pick up on it. It just looks like the slight variations that natural growing hair gets from being out in the sun.

As the piece ages the variation may get more pronounced, and then you may want to get some ash tone colour correction shampoo to take the red tones out. There are various brands available depending where you are. Are you in the US?