Cocci can hit at any age, chicks are more prone to it in the first week, and some say 3rd week. damp chilly conditions seem to invite it. Damp conditions period is what I have seen, stress can also bring it on when a birds immunity is compromised.
My brush with cocci in chickens was with meat birds I brought home 2 years ago. They were pretty dirty, and in muddy conditions. I should not have traded for them. Already 4 weeks old, and I don't think the tractor they were in had ever been moved. I got them home, and in 2 days found them to be droopy, listless and feathers poofed out. I started reading and looking on BYC and realized it was cocci. Got corid, and saved all but one. The only bird that was pooping blood is the one that died.The coop they moved into had not housed animals before, it was a storage shed Dad built with a gravel floor, and only had a few rakes and shovels in it. I have seen rehomed adult birds get it if they are exposed to the ground too fast. Adults I bring in are caged off the ground to prevent that problem too.
Main thing to remember is dry conditions. Cocci can't thrive if its dry. Allow adults time to acclimate slowly to the new flock and what they are exposed to.