Same way a SATA controller works without a BIOS. You boot Windows off some other (bootable) media and the driver loads, and you get access to your drives on that controller. I think most SATA cards have BIOSes though.
ISA IDE controllers without a BIOS work similarly, like the (tertiary) IDE controllers on sound cards, meant for CD-ROM drives. Your CD-ROM driver loads and finds the drive on the correct port and with the correct IRQ. This is also pretty much how a BIOS-less secondary controller works in a system that only has primary IDE on the mainboard. I have a BIOSless ISA IDE card in one of my 486s for this, it's comprised of pretty much all glue logic since it's not super complicated to adapt ISA to IDE.