Khan had guessed that noble representatives were on the planet. He didn't see them in the landing area, but his return and the recent mess made their presence more than reasonable.
After her mishap during the tournament's auction, the Montares family replaced Princess Rachel with Prince Andrew to deal with Khan. Still, the deal probably pleased it enough to reinstate her position. Khan could take that as an act of goodwill and trust, and the plan indeed worked.
Nevertheless, that political maneuver didn't explain why Princess Rachel had appeared inside the room at that exact moment. Khan would eventually have to deal with the noble representatives, but those meetings required preparations and agreements.
Also, Princess Rachel's military uniform hinted at informal purposes. She probably wasn't there on official business, and someone had even told her where Khan was.
