OpenTuna in his actual version is just for use in Slim PS2 consoles and on SCPH-500XX with v1.90 BIOS.
This has not been tested, but assuming that OpenTuna's exploit is like the original Fortuna project, once it is installed on your Memory Card, it is advised to NOT use it on a FAT PS2 console or it could damage the savedatas inside your Memory Card. If you want to use that Memory Card on these kind of consoles, just delete OpenTuna and done.