This is a sedge. I am not familiar with warm season grasses but boy howdy am having to learn more about them. Ugh. I'd hate to have to have a lawn 'down south'...cool season grasses are far more controllable as they are so different in needs to the weeds we normally have. Sedge is a water lover. It is also a 'grassy weed' so controlling sedge will be tough to do.
First thing, I would mow that lawn short! Get rid of those seeds. In fact I am unable to think of other maintenance practices...other than, sigh, preemergence chemicals. They stop the germination of these seeds which are more than likely in your neighbor's yards and will continue to be a problem. If your entire lawn is healthy, you don't live on a slope where this stuff will leach away and off your property, there are herbicides called pre-emergent chemicals to stop seeds from germinating. Here with cool season grasses we can keep our lawns mowed on high to minimize light to the seeds. We are also able to allow the soil to dry out in between waterings as our grasses have deep roots and we are able to promote their depth...weeds usually have shallow roots. Easy peasy. But you've got a weed, actually, for a grass crop...that needs the same things your sedge weed needs...lots of shallow waterings, mowed short.
Go check at a good nursery with professionals that understand your grasses and the need to control these weeds. Can't believe this is the first time I've advised to use pre emergent herbicide but unless someone else more knowledgeable than mesef with your warm season grasses has a better idea then you need to shop for a pre emergent herbicide.
Get those seeds off of those plants. Mow short short short and bag the clippings to put in your compost pile. Bag your clippings with those seeds most definitely. Best and firstus. Find someone who knows about herbicides for your lawn in your area that will stop these seeds from 'emerging' or germinating.