I finished the quest
The Horn of Jurgen Windcaller. The Greybeards sent me to Ustengrav. Upon completion I saw the note from Delphine. In a bid to learn my last word of "Dah" I went to Riverwood since she was the one who left the note for me.
When I meet her, she tells me "You are the one the Grey-Beards summoned and why I did so and so". Which is why she beat me to the horn of the Wind Caller.
Maybe she heard the summons in the story line, when the Greybeards summoned the Dovahkiin and deduced, BUT HOW?
HOW did she know to go to Ustengrav, which is exactly like a lot of Nordic ruins?
And why Ustengrav?