When Timothy rescues Phillip from the sinking ship, the S. S. Hato, he refers to Phillip as "Young Bahss" which is really "Young Boss" written to mimic the way the words sound in Timothy's Caribbean dialect. This form of address was a common practice in the 1940s.
However, as the story advances, the way that Phillip and Timothy address each other changes. Phillip begins by calling Timothy "Timothy" since "he didn't seem like a mister" and also "he was black." So Phillip already has assumed a casual way of addressing Timothy that is actually quite insubordinate, considering the age difference and the time-period in which children were directed to respect their elders.
Timothy begins by addressing Phillip as "Young Bahss," but changes to "Phillip" as their friendship evolves.
The change in their relationship can clearly be seen after Timothy gets fed up with Phillip's childish behavior and slaps him. After this, Phillip asks Timothy if he will be his friend and call him "Phillip" instead of Young Boss. Timothy agrees and tells Phillip that they have always been friends, but changing the way he addresses Phillip, now on equal terms, shows a true friendship beginning to emerge.