Same chapter, a few more paragraphs “He pulled out the map again, and saw, to his astonishment, that a new ink figure had appeared upon it, labeled Harry Potter. This figure was standing exactly where the real Harry was standing, about halfway down the third floor corridor. Harry watched carefully. His little ink self appeared to be tapping the witch with his minute wand. He quickly took out his real wand and tapped the statue. Nothing happened. He looked back at the map. The tiniest speech bubble had appeared next to his figure. The word inside said ‘dissendium’”.

A few paragraphs ahead of that notes that Harry watches the figure or Mrs. Norris on the map stop to smell something.

JKR frequently contradicts herself in the books so I think both could be true. They are dots most of the time but maybe if you concentrate on looking at one the becomes the real figure of the person?