Rosita was saved from the Cybermen by Jackson Lake, a man who believed himself to be the Doctor. They heard about people going missing and decided to investigate. She first met the real Tenth Doctor when a Cybershade was caught in a building. Rosita saved Lake and the Doctor from almost dying. She later told the Doctor about everything that was going on. The Doctor explained to her and the "Doctor" what had happened. Rosita went with the Doctor and even punched Miss Hartigan in the face when Rosita found out what she was going to do. Rosita saved the orphan children who lived at the work house, forced to work the mechanics of the CyberKing. After the Doctor went away she went to live with Jackson Lake and his son.
She was feisty, to the point of punching Miss Hartigan in the face for insulting her. However, she was loyal to both Jackson Lake and the Doctor, even after finding out about Lake's not being who he thought. (TV: The Next Doctor
Rosita is not a companion of the Tenth Doctor, but rather a companion of Jackson Lake, who believed himself to be the Doctor. Nonetheless some media and references list her as a one-off companion of the Doctor's.
According to a digital spy interview with Velile Tshabalala, Rosita was a prostitute before meeting Jackson Lake. This is hinted at in the episode when Rosita and the Doctor confront Miss Hartigan and she replies to her by saying, "You can be quiet; I doubt he paid you to talk".
Multi-adventures reference the rare instance when a companion is shown or stated to have multiple adventures with the Doctor but only appears in a single story.
If a medium is not mentioned, then this incarnation did not have companions who were original to that medium; it does not mean that this Doctor failed to appear in that medium.