The server version shouldn't matter, the database should be universal and can be carried over from any host windows linux or mac.
Though there may be an issue surrounding 2008 > 2012? Not sure.
But it sounds like if it's not restoring correctly there may be an underlying issue.
Getting any kind of errors?
I'm doing this with a PowerShell script but from a 2008 R2 to another 2008 R2 server.
To create a dump file I use:
mysqldump -u $DBuser --databases $DBname -r $Filename
To import the dump file I use:
mysql -u $DBuser $DBpasswordl $DBname < $PathtoDumpfile
The mysqldump creates a UTF-8 encoded file by default. If you edit something in the file before importing it, make sure it is still encoded in UTF-8. Everytime I had a problem with the import it was because of the encoding.