It's not magic, it's covert ops. The Thalmor's spies can use proxies to back promising anti-imperial voices and use those anti-imperial activities to justify further crackdowns which increase support for the anti-imperial movement, and repeat until it gets to a point where the rebellion is self-sustaining, and from the Thalmor dossiers we know that this is literally what they did.
And I don't think it'd be the same outcome. Notably without a noble to stick on the throne there's way less of a path to victory for the rebels. But the thing the Thalmor need to create is conflict that wastes the strength of the Empire during the interregnum, and I absolutely believe they could do that. Scattered peasant uprisings aren't as good as an organized rebellion, but they'll do in a pinch.
Given that in this scenario the most likely leaders are not educated nobles but rather veteran soldiers and well connected commoners I find it easy to believe, especially when the Elves are very prominently backing the other side in the war. The Empire allowing the Thalmor to operate within their borders alongside the Legions works against them. While the Imperial leaders know they're working against the elves, that's not how it looks to an outsider.