Was there a prescribed way to do things in the temple worship?
Yes, temple worship had prescribed ways for everything. The context states that just as Israel moved as an organized army, so in temple worship there were prescribed methods. God is a God of order, so worship was not chaotic but followed specific, orderly practices.
Les explains that when Israel broke camp, they moved as an organized army, not a mob, with each tribe in rightful order. He then applies this to temple worship, saying there were prescribed ways to do everything because God is a God of order. He also notes that even the resurrections are orderly, each man in his own order, reinforcing that God does nothing in a jumbled way. The same principle applies to church conduct, avoiding contentiousness and not appearing as kooks to outsiders.