The side with the burden of proof, the prosecution, always goes first. They will start and split the total time they have for argument between the initial argument and rebuttal. The defense goes after the first argument by the State. So the arguemnt goes: State, Defense, State for rebuttal. If things go like in my jurisdiction.
In this case, the burden of proof falls on the defense - Constitution be damned. A few days ago, one of the prosecution attorneys even pointed this new fact out to the jury, pointing out that Zimmerman had not yet proved 'self defense'.