I'm unsure what you mean by "why". Imperial Shurima was an agressive, expanding empire built on the top of slavery, it was basically Noxus with celestial buffs, less cultural integration and slavery(or at least WAAAAAAAAAAAAAY more slavery).
As far as I know you understandement about how it worked is right.
It became independent some days before they summoned the Void, the IcathiaxShurima conflict was alredy happening for some time when Where Icathia Once Stood(hence the mention of an Ascended killed by the Icathians at the borders of Iathia) but the independence lasted the time the Ascended Host took to reach the Icathian capital.