Ulfric isn't a bad guy in the sense that he is evil as the Thalmor are, but at best his before and after imaginative of Skyrim is most gratitude to his position. Before the rebellion he was a Jarl of arguably the 2nd or 3rd most important city who answered to a King who in turn had representatives in the Empire, whilst after his rebellion he would be High King, and the ultimate authority in the land. It's just a classic power grab, population gets pissed at X issue, a leader arises promising them freedom from said issue, and implants himself on top of the political map at their toil.
Sort of like the first Mede did when he took over the empire? He was just a Colovian warlord. He stepped into a confused political landscape, beat some people down, and did so decisively enough to take power. That's how it works, at least when civil institutions have broken down. The same is true in Skryim. People no longer have confidence in the civil institutions to settle leadership, so it becomes a question of arms.
How does the Thalmor not mater? They are who caused the entire issue in a deliberate attempt to weaken the Kingdoms of men in preparation for their conquest and subjugation. Ulfric is leading his stormcloaks right into the Thalmor trap, and because Skyrim is an province in the Empire, the Imperials sent assistance to try and stop him. No one profits from the siutation but the Thalmor who openly wage a war in everything but name against the provinces.
It doesn't matter because
both sides consider the question of who's in charge important enough that they are willing to take up arms to settle it. People saying "the Stormcloak rebellion helps the Thalmor" are begging the question. From Stormcloak perspective, the empire has capitulated to the Thalmor and effectively are in cahoots with them now, so the fight for independence
is the fight against the Dominion- and a matter of survival.