That's essentially correct, with the following difference in translation from mine:
Minister over the Masses = Prime Minister (Situ 司徒)
Minister of Works = Supreme Censor (Sikong 司空)
Grand Tutor (Jia Xu) = Grand Tutor (Taifu 太傅), and is actually one of the Three Excellencies (Three Grand Ministers)
Commandery = Prefecture (Jun 郡)
Grand Adminstrator = Prefect (Taishou 太守)
The Governors (cishi 刺史) were originally Inspectors in the Han dynasty, roving from province to province to check on the prefects. Gradually their posts became permanent and fixed in one place, so that by the Yellow Turban rebellion they were essentially Governors.
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Military ranks in many cases were just general ranks with an addition at the end generally given according to the person's fame.A general who quelled the Qiang might be "General who conquers the Qiang" or something.The formal hierarchy of these esoteric ranks is impossible to know.Generally the person's overall rank would be established by what they were assigned to do.
The most important military ranks in the Three Kingdoms and Age of Fragmentation, besides more honorific ones like Grand General (or General in Chief, 大将军), General of Chariots (车骑将军) and General of Cavalry (骠骑将军), included the Four Conquering 四征, Four Garrisoning 四镇, Four Subduing 四安, and Four Pacifying 四平 generals:
The General Conquering the East/West/South/North (征东将军、征西将军、征南将军、征北将军) - usually conferred upon a general leading an offensive campaign in that region of the empire.
The General Garrisoning the East/West/South/North (镇东将军 and so on) - usually conferred on a general guarding an important city in that part of the empire.
The Generals Subduing/Pacifying the East/West/South/North (安东将军/平东将军 and so on) - less specific, but usually for offensive campaigns.
Another important post in the capital was the General of the Imperial Guards (中军将军/领军将军), under whom would be the elite Imperial Guards and Palace Guards.
Ghost of Han is correct to say that many of the other titles for generals were less systematic and specific to the situation. The General who Tames the Waves (伏波将军) mentioned by Ghost of Han in his first post, Ma Yuan 马援 of the Eastern Han, received this title for subduing a rebellion by the Vietnamese (led by the famous Trung sisters), who were traditionally associated with the sea.