In the sentences "Jack turns back his head and looks back. He realizes that Chad is getting closer." is the grammar correct?
Context: Jack is running on the street and Chad is chasing him.
You could say "Jack turns his head and looks back." But you don't really need to say that - we don't have eyes in the back of our heads, so we must turn our heads. "Jack looked back and realized Chad was getting closer." (Your present tense: Jack looks back and realizes Chad is getting closer.)