EFI is the software that installed on your hardware. So no matter what you have or have not installed, this software will be there. It's what tells your computer what to start, where to look for the OS etc.
On non Apple PC's they use a BIOS. Windows needs a BIOS. So when you install windows on your mac it fakes it has a BIOS, while in fact it has EFI.
When you option boot (where you can select which drive to start from), that's also the EFI. And since the EFI is installed on your hardware (guess that's the motherboard) it doesn't matter which hard drive you install, it will always have the installer.