Most likely you did nothing wrong. I don't think you could have done anything in one week to have caused this. You didn't replant, change the soil, put into freezing condition, over or under water.
Notocactus isn't hard to grow and take a while to show a problem. You didn't say where you are located. Noto are from lower desert areas but can grow in most locations, many people have them in windowsills or in outside gardens where the weather permits.
You had it for a week, I'd take it back and let them tell you what they think, maybe they'll replace it.