Paths are stored in a tarball relative to where you were when you issued the command to create it.
Code:
tar -cvpf /usr/local/backups/mysqlbackups.tar /usr/local/mysql/data/
Is problematic, but
Code:
cd /usr/local/mysql/
tar -cvpf /usr/local/backups/mysqlbackups.tar data/
will give you an archive that outputs a "data" directory.