Firmware doesn't end up in TM. When applied, it resides in the deep dark bowels of the hardware. As in some corner of the HDD or the SuperDrive controller, some mysterious chip in the logic board, etc. Only way to check it is by querying the component, like the System Profiler does in the system report. Only stuff that might end up in TM would be the FW installer, if you didn't delete it after use.
And when a tech spouts the classical "yer firmwer is nah good" line, many times it is a CYA for not doing what they're supposed to complete.