I’m in Dallas; it’s been roughly 90°F in the mid to late mornings lately. It literally took 3.5 hours for both filters to fully dry, including residual condensation inside, while sitting in the heat of the morning sun. The best way is just to set them aside overnight, but that’s not always an option. If you were to oil them while they were still somewhat [imperceptibly] damp, the oil would be prevented from fully wicking into all of the filter material, resulting in the white or light red areas that you mentioned. On that same note, K&N recommends allowing the oil to wick for twenty (20) minutes.
I just follow the manufacturer instructions, pretty simple, here:
https://www.knfilters.com/instructions/18627B_inst.pdf
ETA I just reread your post. No offense intended at all, but there is no possible way that your filter was anywhere near dry enough to be oiled, you oiled a water soaked filter. That is based off of the time you allowed and your visual description of the filter as you tried to add the oil. It most definitely should have been a consistent dark red color all over, inside and out.
K&N filters have between four (4) to six (6) layers of cotton fabric. Imagine four (4) wet cotton t-shirts layered atop each other, pleated up, and then left to dry in a box with a small fan for only fifteen (15) minutes; impossible. Maybe next time give it a try after letting the filter dry overnight and compare your results. I think you will be pleasantly surprised at what happens when you apply the oil.