Just as an FYI, we're not allowed to call it "Heimlich" anymore. Its the "J-Thrust" or abdominal thrusts now. Copyright issues.
Please please please do NOT pound someone on the back unless they are bent over or are upside down (like a kiddo) I nearly died when someone did that to me. Keep in mind that if adults are coughing, they are getting air and do not yet need you to do anything yet. Kids need us to help because they can panic more quickly. Another vote for learning what to do in crisis situations.
Yes, please, please don't pound an adult on the back who is coughing. I had chronic, episodic bronchitis since I was very young. When I am having a coughing fit, I really don't want someone pounding on my back. People do it all the time to be helpful. It isn't. But, you could ask if they would like some water
Sometimes I just got a drop of saliva down my windpipe.