I think the back-up option is only meant for the files in the folders but I am not sure because I've not used that option.
I guess you never worried about creating backups before? Because then these things also come into play.
First transferring your set-up to another host (and when creating a backup) is dependent on what kind of install you have. MySQL or flat files?
If you have flat file then the necessary files will just transport with the normal file transfer. That's done through FTP. Most servers offer you FTP access. There are a lot of FTP programs around. I use Filezilla.
FTP access gives you the option to up- and download files. By using the last option you can make a full copy of all files on your current server.
Obviously you upload them on your other server to get the file copy.
For the MySQL content you need access to some SQL enviroment where you can create exports of the tables defined in your database of PivotX.
These exports can be imported again on the new server's SQL environment (first let PivotX create it just as if you are setting up a new install).
I guess some flat files copied (for example in db/cache) are not needed so potentially you need to reset those. Looks like you have to experiment somewhat.......
Quality is in the detail of things............