Admiral Ross explains it just before the quote you mentioned. Koval had been working as a Starfleet agent for at least a year.
BASHIR: How long has Koval been working for Starfleet?
ROSS: He's been providing the Federation with critical military intelligence for over a year. When he started working with Section Thirty one I don't know.
BASHIR: But in any case, we have our mole, working for us at the top levels of Romulan government. Good for us.
Since he is working for Starfleet, it makes sense that he would push its interests on the Continuing Committee.
Edit to address Craig's comment below...
It's important to understand a few things...
Koval was never in any danger at all. The assassination plot was made up by Sloan, Admiral Ross and Koval himself. It was entirely fabricated.
The goal of faking an assassination attempt was to bring down Cretak. This would prevent her from taking the seat on the Continuing Committee and allow Koval to take it. This seems counter-intuitive because Cretak is presented as a supporter to the Romulan/Federation alliance. However, this isn't necessarily true because as Admiral Ross puts it to Bashir
I told you before, Julian, she's a patriot. Which means if it served the interests of the Romulans to negotiate a separate peace with the Dominion, Cretak would push that option.
So, she could potentially abandon the Federation if she thought that was best option for Romulus.
The trio of Sloan, Ross and Koval told Bashir about the "plot" in order to manipulate him into working with Cretak. They present Bashir with a seemingly credible plot to assassinate Koval. Then, they remove any Federation allies he might be able to turn to for help (communication blackout with DS9, Admiral Ross's fake aneurysm) which leaves him with a single person to turn to for help: Cretak. Cretak believes Bashir that there will be an assassination attempt. After all, Koval has been saying there is a Federation agent working within the government (plot twist: it's him!). So, she does the "right" thing and accesses the Tal'Shiar database without permission to try to find out who the assassin might be. They catch her and she is convicted of treason for this. Koval's rival is removed and he gains the seat on the committee.
Now, Starfleet has an agent in the ruling body of the Romulan Empire. And he seemingly has every reason to hate the Federation because of the assassination "attempt." So, when even he is pushing for the Alliance, you know it has be good for Romulus, right? The appearance of Koval putting aside his personal "hatred" of the Federation in order to support an alliance against the Dominion gives a lot of weight to that recommendation.