I have part of this problem working offline. I have used Premiere Pro for years and never had this message: "The project file has been modified since the last save ..." until 2/17/ 2019. I have been getting this and saving anyway. Only today, 10 days later, have I discovered the project file I thought I was saving has not been saved. It started out on my external drive. Now I find that it is saved on my hard drive Documents/Adobe/Premiere Pro/13.0/Adobe Premiere Pro Auto-Save/ Shock!! There are files in there dating back to October, 2018. But I never was aware of it, never got this message until February, 2019.
I found a setting in the menu item "Project manager" called "Destination Path" which is the Documents/Adobe/Premiere Pro/13.0/ . Could that be it? I'm going to try changing the Destination Path to be the same as my project and see if I can get Premiere to keep the latest version on the external drive where I want it.
I hope that solves the problem of Auto-Save being the main file. I always thought my project file should be the latest and the Auto-Save was just for backup.