Just because they have the protozoa that causes Cocci is not a cause to panic. There are different strains of the protozoa. At least one strain is obviously in your ground. It is always going to be there. That is important to remember. But chickens can develop an immunity to the specific strain of protozoa. That is actually what you want to happen. Young chicks can develop that immunity easier than older chickens. Immunity to one strain does not give them immunity to all strains. And older chickens seem to get hit harder with it than younger chickens, though it is a danger to all.
It sounds like your older chickens are showing the symptoms of Cocci, so yes, you need to treat them. Once they get over this, they should be immune. That specific strain should not bother them again. How did it get there. Maybe an infected wild bird flew over and pooped. That's all it takes.
The protozoa does not cause any problems unless the numbers get out of hand in the birds' intestines. If you keep the brooder, coop, and run dry, it is usually not a problem. Usually. If the brooder, coop, and run are wet, the protozoa can survive in wet manure and can get out of hand when the birds eat the poop. So if your young birds have been exposed, they may already have an immunity and you don't even know that they have that exposure. You don't want to treat them unless you see a problem. They need that protozoa to survive in their intestines in low numbers for two or three week so they can develop that immunity.
What I would do in your situation (actually I do this each time I brood chicks) is take some damp dirt from the infected birds run and give that to the chicks to expose them to the protozoa so they can develop the immunity they need. Don't obsess about keeping your brooder bone dry, just don't let it get very damp. Of course, watch them closely for signs of a problem and be prepared to treat if necessary, but odds are you won't see a problem. And when they hit the ground where that protozoa is, they will have the immunity they need. Of course, when they hit the ground is another time you watch them closely for signs of a problem.
Many of us have the protozoa that causes Cocci in the ground, especially in the Southeast where it is so hot and humid. It is usually not a problem unless it sets in real wet for a while. Don't get me wrong, Cocci can be serious and can kill chickens. But it is something you can control.
Good luck!