Does the model allow for empathy?

I know that I am responsible for my own emotions, and other people are responsible for their own emotions. I wonder though, how do we truly care for other people if we don’t care about their feelings? My work depends on a large amount of empathy for others and I find applying this aspect of relationship/communication/thinking sometimes doesn’t seem like a natural fit. In fact, sometimes the responses I hear seem a little bit cold. How does the model make space for empathy?