So I had a problem installing this update and I wanted to share how I fixed it. The file that originally downloaded from the web site was called MY15_RA4_15_06_1_NAFTA.exe. When I ran it to extract the file for the update, it created MY15_RA4_15_06_1_NAFTA.iso on the USB stick. I made sure it was the only file on the USB stick and inserted it in the car, but the system didn't recognize it as an update file.
After doing a little research I saw that in the past the ISO files were named "swdl.iso" so I renamed the ISO file on the USB stick to swdl.iso. The system did recognize that as a valid update, and updated the system to version 15.06.1.
So if anyone else gets hit with this, make sure that the update file is named swdl.iso. Hopefully Chrysler will catch this soon and update the file on their servers so it'll just work without having to be manually renamed.