AHCI/IDE settings doesn't affect bootloader. Grub (or Windows bootloader) works with both AHCI and IDE modes.
For Windows these modes requires different drivers: SATA for AHCI and PATA for IDE. Once Windows kernel loaded, it uses appropriate driver to work with HDD. Switching from AHCI to IDE affects only when kernel is loaded, it isn't boot issue.
Instead of Windows, Linux has both SATA and PATA drivers built in kernel, so for Linux it doesn't matter is HDD mode set to AHCI or IDE. That's why you can switch it and Linux still boots.
Anyway BIOS works with both modes, if HDD has boot code, BIOS will start it. Otherwise BIOS will try to start other devices and network.
Seems your Grub this time was installed properly when you reinstalled Mint.