I don't have wild cats but we do have 3 farm cats who hunt rabbits, bird, and mice like they are standing still. They only play with the chickens, they seem to get pleasure out of working the hens into a tizzy. I have never seen my rooster take after any of them so I don't know if it is just a mutual respect thing or if the rooster helps. I think it may be of similar to our dog who doesn't chase our cats but kills ones that stray to our place.
If i were in your situation I would lock the roosters away for a couple days while you can keep close watch and see how it goes.