On the site you reference, XP only has one entry, so not divided between x64 or x86. If you are using x64 XP, are you sure it is both versions? And you don't have to extract anything, since the Driver disk is set up, unless this is necessary for the x64 version.
When you use nLite, are you selecting the AHCI driver for your SATA controller? There is normally a listing for RAID and AHCI, so try using the AHCI one.
One place I saw also mentioned you need XP SP3 to be able to use the AHCI drivers. But using the wrong one will normally Blue Screen. The "not correct version" is probably a x86/x64 situation.
XP will normally need IDE for a controller option without the correct drivers.
Edit: I checked the readme file on the F6 disk and it states the drivers are good for XP x64.