One of my favorite commentaries on the Bible is written by a down-to-earth man named J. Vernon McGee. Speaking of this passage, he put it this way: "Believing in God doesn't make you a Christian."
I suspect the order of the reforms Josiah made were responses to the things God helped him to see. The faith that opens our eyes to our need for Christ's work on our behalf grows expands as the years go by. Each response of surrender, each step of obedience, reveals a new one. The Christian life is one of continual cleansing--the work is never done. The indwelling Spirit is the first-fruit not the harvest. And the glory of that harvest belongs totally to the Lord. Thankfully receive His gifts and allow His work to go forth--showing the next step at just the right time. He'll produce a glorious result without us ever knowing the total program ahead of time.