Gain increasing amounts of AD or AP, Adaptive over the course of the game.
Azir loves to auto attack with his soldiers, especially with his most recent changes. With Lethal Tempo you're able to scale into the mid-late game as an incredible hyper carry.
WhyPresence of Mind
Presence of Mind is a great lane/teamfight mana sustain rune, allowing you to spam, so long as you're taking advantage of it when you level up or get a kill/assist.
Doubling down on Attack Speed, Azir scales incredibly well with Legend: Alacrity and auto-attacking with his [W].
WhyCoup De Grace
Because Azir often builds a few health items (Rylai's/Liandry's) he is not able to make complete use of Cut Down against carries, so Coup De Grace is your best bet for ending the enemies lives as quickly as possible.
More CDR means lower [W] cooldown which means more soldier. All of your damage in this loadout focuses on having soldier out to auto as much as possible so you're going to need the CDR.
Gathering Storm on Azir makes him an incredible late game hyper-carry. A little Magic Penetration from items and Attack Speed from runes and Gathering Storm brings all the extra AP you'll need to carry.