Tanya's form of exit announced that the game had changed just enough to give the Harons a semblance of gaining ground on the Sapphirine Cult.
Tanya had opened herself to the power of the gem to the point where she could transport her entire self into the monument of Ordinances at any given time.
The reason why the portal she had escaped with had been so easy to recognize was that it was the same portal that anyone entering the Monument of Ordinances would have to go through and after strengthening the connection between herself and the gem and the gem and the monument of Ordinances, Tanya could manipulate that opening wherever she was.
She then combined that means of entry into the Monument with the perception she had over the landmass of the Haron Continent to pinpoint locations in which she wished to exit at.
Basically using the Monument of Ordinances as a medium with which to cut short the journey between regions on the continent.