It refers to a person who is worrying too much about others' evaluation.

As a consequence, 自意識過剰な人 can appear as either narcissists or shy worriers, but I think their appearance is not important. Even when this term is used for "narcissistic" people, it implies they are not fully confident, and they are trying to beautify themselves out of unnecessary anxiety.

It refers to a person who is worrying too much about evaluations from others.

As a consequence, 自意識過剰な人 can appear both as narcissists and shy worriers, but I think their appearance is not important. 

Even when this term is used for "narcissistic" people, it implies they are not fully confident, and they are trying to beautify themselves out of unnecessary anxiety. On the other hand, a true narcissist does not care about other people's criticism.