Not much is written on Kronos hierarchy (at least not outside his own archives). What is available can be found in Revelations III.
Kronos uses titles of nobility for his higher distinctions. Officially each title matches the Word of the Servitor that holds it (Kronos only considers Wordbound demons for his highest distinctions). However, a powerful word is not enough for promotion within the Archives. A demon must also know their own motivations and know that they can best serve those motivations by serving Kronos (actual loyalty is too much to expect, and Kronos probably would not trust someone who showed it).
And as far as outside duties go, that is entirely accurate.