One of the major factors that got people moving was likely the images that came out of Hurricane Harvey and all the people who needed to be rescued. That got people over the inertia of "not moving." Then, many others were evacuating which then caused more to evacuate.
Fortunately, there were no major incidents or deaths that I heard about from the evacuation. It is hard to be in a fatal car crash going 5MPH! And, I think the State of Florida did what they could to keep gas stations supplied with fuel. I know that they also stationed porta potties at rest stops and other locations to handle the extra traffic.
Lastly, how many people died from staying in place and not evacuating? In my book, the evacuation was successful.