Is there evidence that Phillip is the narrator?

Yes, there is evidence that Phillip is the narrator of The Cay. The first evidence presented to readers is the second sentence of the book. 

I was asleep on the second floor of our narrow, gabled green house in Willemstad, on the island of Curacao, the largest of the Dutch islands just off the coast of Venezuela. 

As the previous sentence shows, The Cay is written from the first person perspective. Phillip is narrating the events of the story retrospectively. This means that he is telling the story after all of its events have happened. A reader knows this because Phillip is using the past tense. The first person point of view gives readers great insight into what Phillip is thinking and feeling. Unfortunately, the first person narration does not give much insight into what other characters are thinking and feeling. It works well because we really get to know, understand, and feel Phillip's fears once on the island, but it would be nice to have more knowledge and insight about Timothy.