I'd read the TES books, but from what I remember, Black Marsh is its own nation, free of Imperial and Thalmor influence. The Saxheel are independent, and wish to remain independent. They took portions of Southern Morrowind, likely swamp land held by Dres.
After the Crisis, the native Saxheel faction, similar to the Stormcloaks, took over and began to remove Imperial influence. In addition, the Thalmor tried to gain a foothold by inciting the war against the dunmer. However, it backfired as the Saxheel immediately kicked out the Thalmor once they got what they wanted (southern Morrowind and driving away the dunmer, as they were a threat against Black Marsh).