Zimmerman didn't need 'going to kill me' under Florida Law. Under Florida Statute 776.012(1), Zimmerman was permitted to use deadly force, with no obligation to retreat, to prevent 'great bodily harm' to himself.
Florida Statute 776.012: "[A] person is justified in the use of deadly force and does not have a duty to retreat if:(1) He or she reasonably believes that such force is necessary to prevent imminent death or great bodily harm to himself or herself or another . . ..
I linked the full Justifiable Use of Force statute above. I haven't researched to see if a Florida court has interpreted 'great bodily harm' under this context or another context yet. Those would be the next steps I'd undertake in a legal analysis.