That article referenced goes into detail about that. It started with a genetic difference from when deer were moved here and the climate difference has not required that to change. In other words fawning can occur later without negative effects. That's what I gleaned anyway.
That article references some very good research on the topic. However, I'm not a total believer in the idea that the odd breeding dates in the Deep South a driven by where deer were restocked from in the early 20th Century. I say that because deer in TN were restocked from all over, and some of these stock locations have VERY different peak breeding dates. We had deer brought in from TX, NC and SC (both the mountain regions and the coastal regions which have very different peak breeding dates), and even MI and WI. If all those unique breeding dates held where those populations were released, we would have a hodge-podge of very different peak breeding dates scattered all over the state, with one county having a peak breeding in October while a neighboring county in December or January. But we don't. In fact, for most of the state, we have a smooth transition, with the earliest peak breeding in the northcentral and Nashville Basin area, and then slowly growing a few days later and increasing with distance moving east, south, and west from Nashville. The only big differences occur along the MS and AL lines, where peak breeding can be significantly later. A fairly smooth but also fairly rapid transition in dates occurs from Jackson towards Memphis, with dates moving into mid to late December near Memphis. This is not the pattern of "remnant DNA" controlled breeding dates. This is the pattern that would develop if a naturally occurring influence such as temperatures, timing of food sources, or something similar were the driving forces.
Now I have to admit, I have no idea why the insanely different dates occur in the Deep South (especially AL, MS, and LA). Some of those are crazy. But vastly different peak breeding in some parts of the South, such as the coastal regions of VA, NC, SC, as well as south FL and southern TX are easily explained by environmental conditions.