If Izzy is heading due N or NNW when passing by the Florida west coast, evacuations would probably not be ordered for those areas. Possibly would be only for the lowest lying areas. This would depend on the confidence in the forecast, and forward speed, mong other things. Even at 100 miles or so offshore, it would take some time for an Izzy to turn around if he was moving at 15/20mph. During Elena in 1985, comparable in size to Izzy, I was driving around in some horrible weather while Elena was heading N. When she stopped and started moving E, evacuations were ordered and completed before she got within 75 miles or so. Can you turn your car to the right once you are in the middle of the intersection? Only if you are moving pretty slow.
Hope the analogy helps. Incidentally, you may want to look up Elena accounts on the web. Izzy probably will be a very similar storm.