I have the mini display adapter plugged into the back of the Thunderbolt display, as the Thunderbolt display is plugged into the Mac Mini.
Am I doing things wrong?
You probably are burninglegs. Check this information from Apple Insider:
http://forums.appleinsider.com/t/13...t-display-will-not-daisy-chain-cinema-display
"However, users with an existing
Mini DisplayPort external monitor will not be able to daisy chain the screen from the back of the new Thunderbolt Display, despite it being physically compatible with the port. Apple notes that "Mini DisplayPort displays will not light up if connected to the Thunderbolt port on an Apple Thunderbolt Display."
Existing Mini DisplayPort screens, such as Apple's LED Cinema Display, have never previously supported daisy chaining multiple screens to a single Mini DisplayPort interface, but the screens are supposed to work at the end of a Thunderbolt chain if there are no other displays in the chain."
Your MDP adapter will work in some configurations but not when daisy chained after an Apple Thunderbolt Display.
The good news is that the USB powered adapter I mentioned in the prior post is only $29!