Over time, scientists have noticed that some hurricanes and tropical systems generate areas of heavy rain far ahead of the main storm system. These events are called Predecessor Rain Events (PREs) because they generally occur about 36 hours ahead of the main storm passage and as much as 600 miles poleward of the storm center. The presence of a front in the area along with a strong moisture flow from the storm can enhance rainfall in this region, leading to potentially heavy rains that can cause flooding or set up the region for flooding once the main storm moves over the PRE region. Note that PREs do not have to form near the coast, but have formed as far north as Wisconsin and New England as the tropical cyclones moved inland along their paths.
The weather pattern for Zeta looks conducive to the formation of a PRE, which would bring an area of heavy rain to an area north of the Gulf sometime on Tuesday. At the moment, the models do not all agree on where the heavy rain is likely to occur, with some putting it farther west over Arkansas and others putting it farther east over MS, AL and GA. If one does occur in the Southeast, it could provide heavier rain on Tuesday afternoon or night than currently forecast, which bears watching. If the ground is saturated by rains from a PRE, then flash flooding would become more likely on Thursday as the storm moves north through AL and GA.
If you are interested in reading more about PREs, you can find a journal article about their climatology at https://journals.ametsoc.org/mwr/article/138/8/3272/71161/Predecessor-Rain-Events-ahead-of-Tropical-Cyclones.