Here's what I've gathered on Winterizers from this group and others, esp for your area. I'm not a pro by any means but have been learning a lot asking these same questions as I'm learning about growing TTTF in the deep south.
There are generally 2 fall applications: an early fall one (around over-seeding time, which is meant to encourage recovery & growth) and a late-fall application (typically falls around mid-late Nov for your area, after the grass stops growing but before the ground freezes). Whereas the first application needs to last you +/- 8 weeks (or you can follow the fall nitrogen blitz idea and apply quicker-release fert at shorter intervals over this same time period),
the last fall application has a shorter window before ground freezes and nutrient uptake is no longer possible (and whatever Nitrogen is left lingering on the surface will leach out, unused by the plants). If you can get the plant to absorb the N it will hold onto it through the winter. In the meantime it makes the plant hearty overwinter and allows it to come out of dormancy with vigor come warmer temps.
The bag of fert you posted, as Green mentioned, is ideal for a longer-duration release timeframe (perfect for that first fall app) because it has been manufactured with a lot of extra steps and materials in order to encapsulate the volatile urea so as to have a controlled release (6-8 weeks, +/-). It's generally much more expensive for this reason ($20-25 vs $40-50++). Because the ground will freeze before the full release of the nutrients you're not only wasting the nutrients that were captured & manufactured into that fert but also supplying these chemicals into the ground at a time when they'll simply leach into the groundwater, etc. For this reason the suggested product is a quick-release Urea or Ammonium Sulfate fert for this late fall application. *note: because these recommended products are not sold at big-box stores and some ppl don't have direct access to them, the big-box fert with 15-20% slow release is a compromise.
Here's a basic explanation on the PCSCU process btw, in case you appreciate the details as I do:
