Fluorescent light can have a greenish tint, so it may be necessary to add magenta with the tint slider to compensate. Also, you may find times when reflected light introduces a color cast, such as green light reflecting off trees and grass. If there is red tinted light reflecting off red painted walls, a red brick building, etc., you may need to add green to compensate.
It is important to set the temp and tint sliders early in the editing process. They can impact the exposure, so you'll want to pick a profile and set the temp and tint sliders prior to fine tuning the tone sliders. Also, we quickly become desensitized to color casts, so you if you look at a tinted image for long while doing other edits, you might not even notice the cast until your eyes have had a break.
If you are shooting under mixed lighting conditions, you may want to use more advanced techniques at time of capture, such as gelled flash or plan to blend luminosity layers in Photoshop, etc. I would be delighted to help you learn these and other techniques.