She was chosen by Rhombur Vernius to be his concubine when he and Duke Leto Atreides I arrived on Wallach IX for Rhombur to choose a mate. Tessia won Rhombur's heart from their first encounter together.
As Rhombur experienced the grief associated with the loss of the prestige of House Vernius, and their fiefdom on their home planet of Ix, Tessia was a constant source of inspiration and strength to the displaced nobleman. Later, when Rhombur was tragically scarred due to the assassination attempt of his sister Kailea Vernius on Leto, which resulted in the death of his nephew Victor Atreides; Tessia was the first to encourage Rhombur to have the will to live on.
Re-Established on Ix
After House Vernius was re-established on Ix, and the subsequent expulsion of the Tleilaxu, the fortunes of Rhombur and Tessia rose accordingly. Later, Tessia was impregnated with the sperm sample from Rhombur's dead half-brother, Tyros Reffa, to secure an heir for Vernius, and the child was named Bronso.
When Rhombur and Tessia attended Leto's wedding to Ilesa Ecaz, that Bronso had copper-colored hair, and the three seemed very happy.
Behind the Scenes
It was never established in any of the novels as to whether Tessia had any orders from the Sisterhood to influence Rhombur, or to guide him on any certain path. She was simply presented as someone who constantly had Rhombur's best interests at heart.