One might argue that the Feds did it because they thought that the flip side would prove useful for them.
Perhaps the Feds were desperate to hunt down war criminals from the recent Cardassian nastiness, and the Klaestron allowed those to be captured and taken to the UFP without bilateral case-by-case understanding only if the Klaestron society could do the same to criminals hiding in the UFP. And the Feds were willing to risk that, because they thought the Klaestron would never be able to get their hands on a criminal the Feds didn't want to let go.
Or perhaps the unilateral right was empty words only, and any Klaestron attempt would be stonewalled by UFP legal gobbledigook and, if need be, Starfleet phasers? It's not as if Sisko ever seriously considered respecting the warrant that Tandro presented.