There is no "BIOS microcontroller". The BIOS chip is just flash memory. All execution is done by the CPU.
When the processor comes out of reset, it begins executing from a fixed address (called the reset vector). That fixed address is mapped to the BIOS flash chip.
Once the BIOS has completed its boot time tasks (hardware initialization, POST), it begins enumerating boot devices in the order specified in the BIOS setup. The first boot device it finds with a valid boot sector, it begins executing it, and thus control of the computer is handed over to the Operating System.
One other comment, based on your comments: CMOS is just a set of registers inside the chipset that are backed by the RTC battery. They were traditionally used to store BIOS settings, but in a modern UEFI BIOS your settings are stored in flash.