Phillip is initially hostile toward Timothy, because his mother has influenced his inability to react in emotionally appropriate ways to situations.
Phillip is emotional, and he seems to take after his mother. She appears to be an emotional woman. Granted, the family is going through an emotional time, because the story is set during World War II, but she does not demonstrate a lot of stability in the beginning of the novel.
Then I talked to my mother about staying on in Willemstad, and she became very upset with both of us. She said that we didn't love her and began to cry. (Ch. 2)
For a grown woman talking in front of and to her child, this is a great deal of immaturity and seems to be disturbing behavior. It does explain some of Phillip’s immature and disturbing behavior and his own lack of stability. She lashes out, he lashes out. The fact that this is not a one time situation can be traced to the fact that he also says, “My mother was very calm, not at all like she was at home” (Ch. 3) during the evacuation. A lack of emotional maturity is commonplace with her.
When Phillip finds himself separated from his mother, he is frightened and confused. He was with his mother, now he is with a stranger—a black man. He is not used to such men.
I knew he was West Indian. I had seen many of them in Willemstad, but he was the biggest one I’d ever seen. (Ch. 3)
While his mother has influenced his behavior, his father has too. His father has tried to teach him to treat people with respect. Timothy does not deserve his respect, he decides, because he is a black man.
My father had always taught me to address anyone I took to be an adult as "mister," but Timothy didn't seem to be a mister. Besides, he was black. (Ch. 3)
Obviously this is a racist response. It is also part of Phillip’s lashing out. He is lashing out at Timothy in his mind, because Timothy is not his parents. He is being nothing but kind to Phillip, and treating him with respect. Phillip is not returning the favor. The things he is thinking about Timothy are not polite, and only get worse.