A public, well-written online review from a customer whose stylist failed to follow direct instructions and sported an attitude while taking that customer's money (like the OP's stylist) kills two birds with one stone by simply writing online reviews:
1. They warn potential clients about that stylist's potential to do the same thing to them.
2. Online reviews are superb at grabbing management's attention far better than just about any personalized offline complaint (except maybe a complaint launched by a TV station). When complaints are publicized, it's the best motivator for management to deal w/problematic stylists because critical reviews directly affect the reputation of her or his establishment.
So no, it's not economically or logistically practical or necessary for the customer to go all the way back to the place that ruined their hair to inform the manager of what that manager should have already known via careful observance of her or his staff anyway.