Fight or flight response
Thank you for posting this!
To answer your question: Yes, I have experienced a similar sensation. Some advice: Have good boundaries. You are in a role at work, and this role has certain responsibilities. It's hard when you're an empath, because you empathize so much with people. but keeping that boundary will make it easier. You're not punishing anyone after all- you're just playing a role, a role that isn't harming anyone :]
PS: Your post made me realize something about myself. I always have found that I don't like confrontation, and during a debate, I almost change my opinion sometimes. I didn't realize it, but it is for the reason you said- that I feel so in tune with others that I really "get" their point of view. Thanks for mentioning this!