Don't get on the soil if it is wet! First rule.
Depending on what you planted for fall, you may not need any fertilizer. Soil test fertilizer recommendations are intended for farmers with very different goals than deer managers or food plotters. It is fine to start there when you are starting out, but over time I've learned that reducing or eliminating tillage, choosing a smart combination of plant, and getting the pH right can be sufficient. Eventually, you will be able to let your results tell you what you need. I'm to the point where I have not used fertilizer for a number of years and I'm on marginal soil.
As long as you are not getting on wet soil, you can fertilize now. It won't hurt anything. The pH is a bit high for most crops we plant for deer. That is uncommon for most of us. You did not mention the acreage, so we don't really know how much fertilizer is required from your post. You are fine to simply broadcast that fertilizer for now, but in the long-run, you will do best learning about your soils. It is fine to hand your soil test results to the coop guy when you are starting, but it is best to try to understand them. Soil science is not for the timid. I've been slowly learning for quite a few years.
Start by googling "Ray the Soil guy" and watch some of his videos. Start with infiltration. He is focused on farmers with large equipment, but the underlying soil principles are the same. Crimson N Clover has a good Throw and Mow thread. There are other folks on here that can provide a better explanation of your test results than I can, but learning about this has saved me a lot of time and money.
Thanks,
Jack