Later, more isolated storms will fire to the south and threaten the Florida peninsula. While they may be more isolated, the environment will also support the potential for strong tornadoes. The risk may not be high for Tampa, Orlando and Melbourne, but if you're unlucky enough to be in the path of a potentially tornadic storm, assume it'll produce significant tornadoes putting you at risk.
Areas north of the high risk may not see an obvious environment supportive of tornadoes because of the widespread rain in southern Georgia. However this system is unusually far to the south, and our collective experience, limited. Thus I suspect that even western to central Georgia may see a tornadic threat as the surface low deepens dramatically to something rarely seen in central GA - up to five standard deviations below normal for this time of year. Outside of hurricanes, the sea level pressures will be very low down into FL as well. As a result low-level winds will be strong and that means that if you're experiencing a cloudy, cool rainy atmosphere now, that may change quickly to one favorable for severe weather very quickly. Residents in the Huntsville, AL area on the super tornado outbreak day of 2011 can relate to that. Temperatures were in the 50's all afternoon and then in the last hour, jumped to near 70 deg F quickly followed by a mile-wide long-tracked tornado.
Furthermore, the probability that any one supercell will produce a significant tornado currently stands in the 15% range according to research by Smith and Thompson and Marsh of SPC in the last few years. Get used to those numbers being extremely high. As cases are gathered and return intervals calculated, you may see them as rather unusually high. More importantly is that these numbers will go up from here as the day progresses. The key thing to consider is that area hodographs feature large storm-relative helicity, very humid atmosphere (in an absolute and relative sense) and lots of buoyancy for thunderstorms to grow uninhibited, as seen from this sounding from the HRRR in the FL Panhandle ahead of the storms.
Bottom line, if your sheltering location is dusty, or cluttered, clear it now!