Azir's soldiers's auto attack procs Thunderlord Decree?

Yes.

EDIT: I've actually been using 12-18-0 masteries on Azir for the mana regen and higher CDR cap. The extra damage from Thunderlord's hits like a truck considering what you trade for it.

It is probably the best keystone mastery for Azir as its hard for most champs to make use of Deathfire Touch effectively, not to mention you get that 5% cdr