After much trial and error, I discovered what the problem is.
Evolution on Fedora 18 (which is what I was running) uses Evolution 3.6. Evolution on Debian 7 uses Evolution 3.4. So from my reckoning, you can't restore your data from a newer version of Evolution to an older version.
The work around that I managed to do was unzip the .tar.gz backup file, which should leave you with 2 folders: .config
and .local
. I copied the contents of both folders to their respective folders on my laptop, and I retrieved all of my emails. However, the settings for the email accounts weren't transferred.