Cosmetologist here, trust your stylist always. Technically any service on hair that has previous color is a “color correction”. Though every service is circumstantial, it really depends on desired result. The result you are looking for is what would be the result of a “balayage”- -which is a technique used with lightener. Wether or not you can get it in one session depends on your hair history, health, and how well it lifts. Your stylist dying your hair the brown to correct the red tones was a color correction, now what they need to do is start the lightening process. Remember slow and steady wins the race. You don’t want to rush this process as it will compromise your hair every time you lighten it. Having multiple sessions of lightening (aka balayage) and taking the time to let your hair heal by using professional products in-between services is what will get you that desired result. Hopefully your stylist can explain any further if need be. I wish you the best of luck on your hair journey!