Talos did that. It's funny how the Stormcloaks start a war for a man who handed over Skyrim to the Imperials to gain status as an Imperial general.
From Stormcloak perspective, the empire of Tiber Septim no longer exists. It's mentioned in the history of the 4th era that when the Septim dynasty ended and Mede fought his way to the emperorship, Skyrim accepted him because he had proven himself worthy of the job. The fact that that is mentioned, though, means it wasn't a given that Skyrim was going to accept a new dynasty.
Except, as others have already pointed out, it isn't.
In the Roman Empire, there was nothing like Skyrim is to the Septim Empire.
Agreed, it's a different situation since Skyrim was basically the beginnings of the empire. The closest equivalent, I think, is the rebellion of the Germanic tribes at Teutoburger Wald. Germania was occupied territory, but the Cherusci had been made into Roman foederati, one step away from being Roman citizens. The leader of the rebellion was an officer in the Roman legion who turned on them.
As to the OP's question, I think it definitely can be called a civil war, since Nords are fighting Nords. However there is an aspect to it that resembles a foreign occupation- namely that the imperial governor was called in from Cyrodiil, and some of the legions fighting are also from there. Though Skyrim helped found the empire, in practice the Cyrodiils have been acting as a ruling class.