No worries, it is a bit of an obscure problem. Hopefully the screenshot and the explanation below will make it clearer.
In the screenshot I am displaying a directory in the .Rproj.user directory on a computer that has been copied onto it from a second computer. You can see that the prop subdirectory has an INDEX file. This file contains a list of all the files that were open in the Source panel when I last closed this project in RStudio on the second computer. The following is an example of an entry that shows that I had a file called plotResults.R open (there are other files listed in INDEX):
d%3A%2FAnalyses%2FResearch%2FTPA%2FGrowth%20analysis%2FplotResults.R="4D133B9F"
If I open this project on this computer, then no files are loaded because I have not loaded any files into the Source panel on this computer for this project. On exiting the project a new directory is added to .Rproj.user, the name being 15CDAC0A.
Ideally, RStudio would use the INDEX file in D:\Analyses\Research\TPA\Growth analysis.Rproj.user\B830CA0C on the current computer to open all the files in the Source panel that had been open on the second computer. I cannot see a straightforward way to do this.
Cheers, Chris