Feeling an emotion

Is it important to feel the emotion even after realizing and identifying the thought that is causing it? If so, why?
As I am practicing the model, I am quick to take control that it is my thought causing me to feel this way and identify what I am telling myself. Then I tend to quickly find the thought I can choose to believe and work out an intentional model. Is this not the right way to use the self-coaching model?
Thanks in advance.