Azir's auto attacks via soldiers are overall much, much closer to auto attacks in terms of what its like to play as and against him. For the same reason we have minion agro on regular auto attacks (guaranteed to hit, resource free ranged damage) they need to also pull agro. They apply spell effects in particular because applying on hit effects would be excessively powerful. AOE red buff, Triforce or Lichbane at that range etc are incredibly powerful effects that define how a champion has to be balanced (see: Ezreal) and that wasn't what we wanted to create with Azir. AP itemization also made more sense with how we wanted him to play (not going glass AD or bruiser for example which AD or on hit offensive paths can tend to), giving the right sort of defensive tools and a sustained damage pattern.
Having said that, yeah, there's definitely a bit of clash with expectations in that soldier attacks are treated somewhat as auto attacks and somewhat as spells. The alternatives are really high cost though, so while we do feel consistency's important it doesn't trump everything else. Some degree of rule breaking on any given champion's also ok, or in many cases ideal (it's how champions distinguish themselves from others of the same class).