I recently started using 0.9.3, first on a new 3.6 single user after getting it configured it works correctly with minimize.
Then I did a manual upgrade on a 3.1.3 by first renaming the W3TC directory and then installing the new files from the 0.9.3. Minimize works fine.
I also had an old 2.7mu where I tried to get 0.9.3 to work but had too many missing functions and fatal errors, so I upgraded 2.7mu to 3.6 and then manually installed 0.9.3 and minimize works fine on all of the different blogs, they also all run different templates.
So to sum it up that's 3 diverse uses of 0.9.3 that work correctly with minimize.
Perhaps you have a configuration problem or there is some leftover file from when you upgraded?
Craig