Firmware updates are handled differently by each OEM. For example, Dell includes AMT firmware updates (if available) as part of their BIOS updates. HP, on the other hand, distributes AMT firmware updates separately from their BIOS updates.
I have successfully automated the distribution of BIOS and AMT firmware updates to HP and Dell systems. I can't speak from experience regarding IBM/Lenovo's firmware update methodology.
What kind of systems do you have? This information will determine your strategy for deploying AMT updates.
Keep in mind that the version number you see at the top of the MEBx (Ctrl+P screen) does not necessarily match the actual AMT version on the client.
If you're running BIOS A12, then you will have AMT 3.2.2, which is the latest available for that hardware platform.
You can validate the firmware version using MEinfowin, which is downloadable from IBM: