You'll be fine claiming them on your 2019 taxes, provided they will not be submitting their application until after the new year. If they've already submitted their application you can still claim the dependent. It just raises questions and a bit of a delay once their application comes up for review. Then so long as you do not claim them in 2020 it's really not a problem for you to claim on your 2019 return provided of course, they actually qualify as your dependent either under the qualifying dependent child rules (if an undergraduate student) or the qualifying dependent relative rules.
Basically what happens during the application review process they'll see on his tax return where he indicated he could be claimed as a dependent on someone else's return for 2019. Then the state HUD authority will want verification that they will NOT be claimed as a dependent on another return in 2020. That's all really.
Do note that if the person is in FL for the primary purpose of attending school, that alone does not qualify them as a FL state resident. Doesn't even come close.
