Sounds something like Pandora's Legions by Christopher Anvil. The aliens are not all that felinoids though, I remember them more simian-like.
The Centrans conquer Earth, then discover that humans are way smarter than them; the humans piggyback on the invaders to conquer (economically at least) the galaxy.
The story (more precisely the same collection of stories plus two mid-size novellas) begins with "Pandora's Planet", where the "genius" of the humans was discovered. No galactic trouble is laid down - yet (foreshadowed? You bet).
This first story has a premise somewhat like The Road not Taken by Harry Turtledove - the humans never discovered a very simple way of space travel and antigravity, which every other race did, with the consequence that all those races built a Galactic empire with seventeenth century technology. Then, their ship lands on an Earth with automatic rifles, missiles and nuclear weapons expecting an easy conquest.
(The "very simple technology every Earth scientist overlooked" is also a plot point in The Greks bring Gifts by Murray Leinster).
In Anvil's series, the Centrans decide to exploit the Earthmen's ability and ingenuity in waging war, employing them as janissaries, and giving them access to their space technology for that purpose. After all, what could possibly have gone wrong? These are Pandora's Legions.