In my yard, they don't build mounds; instead they infest my raised beds. This means that you don't know they're present until they swarm out to attack. I've used Amdro and Logic, but because my neighbors won't treat the ants are an ongoing problem. Another organic solution is a mixture of liquid agricultural molasses and orange oil (the problem with this is the orange oil hurts the earthworms). The ants move on immediately (those that survive the drench). The interesting thing about using the molasses/orange oil solution is that it improves the soil. One spot in a bed was particularly attractive to fire ants and I treated it multiple times over a year or two . . . voila . . . that's now the "best" spot in the bed for plants.
Yeah, that's the only time I see fireants in my yard is when I'm digging in a bed. Thankfully those instances are few and far between. I applied nematodes to the yard when we first moved in a couple of years ago and I'm convinced that help keep the lawn fireant free; unfortunately, I didn't treat the flowerbeds.
I've heard the molasses and orange oil mixture works - Howard Garrett recommends that method, I believe.