He is telling the story in the past, but why does he mix present tense, present continuous tense and past tense together?
Good question! He mixes different tenses here because he is telling a story. Although the story happened in the past, he is describing the events in parts as if they are happening in the moment. When you are telling a story or giving a narrative, it is usually okay to mix different tenses together, because it makes the story interesting and it allows the listeners of the story to better imagine the scenario of the story and feel involved.