Those are the colors yes. There is no first and last, just doing the right things with the right books. If you get stuck you can reset by using the purple book
Viewing post in Joseph Earnwile III Chapter 5 - In the Caves of Sorrow. comments
You get two notes, one from each of the girls. They tell you some steps to take. The last clue is the mural. It will tell you about some arrows painted on it. SPOILER:
Green duck, so green book. Duck dives four times, then spin = push four times, then turn once.
Fox is red, so red book. Fox jumps three times, then digs = pull three times, then push once
The arrows are painted in the blue water, so blue book - one of each
The purple book gives you "A New Beginning" - resets the puzzle.