The ability to backup and restore saves from USB does not enable the exploit to be installed at all, that is now how it works
easiest method to use is SwapMagic 3.6 and up over (SwapMagic 3.8 Coder being the best version to go for though) that supports booting from USB directly (no disc swapping)
Older versions of SapMagic can used but using it to boot a CD or DVD instead with ulaunch on it
Action Replay Max Evo can also be used without a disc swap
older versions of Action Replay need to be used to boot a CD-R though (swap trickery needed) using the AR as a boot disc to make the swap go smoothly
Xploder I am not even sure that could be used at all
Code Breaker 8.1 and up over has usb backup and restore features
http://bootleg.sksapps.com//tutorials/fmcb/ is a good place to look and see how it works by looking at Installation (gives an outline of boot methods for the installer)
P.S, you do not need USB save data copy features to install the fmcb mod though, most the methods use a Swap trick of some description to boot a CD or DVD that can install from USB using the homebrew ulaunch to run the fmcb installer from USB or use some other method to run ulaunch
The devices that can boot code from USB just run that installer directly from USB
Being able to copy save from USB to MC does not help you install the mod
Note the last version of the PS2 blocked Memcards from being able to use the mod/exploit
P.P.S. Codebreaker is the best method to backup and restore saves, but again the ability to do so does not enable the exploit to be installed though
I have a full step by step guide up for the actual install process anyway once you get past the boot method for the installer