No, the Toto Aquia doesn't work with the Unifit Adaptor. It'll only work with a 12" rough.
You can find teh mounting hardware here. However, the Push Button is only available in Chrome for this toilet.
In most cases the back sides of Toilets will not be glazed. One option if you are having issues with condensation would be to purchase an insulated toilet. This unit will not be available with an insulated tank but you can click here to view one of our most popular insulated tank toilets. The Aquia model is a standard rim wash toilet which means the water will come from under the rim of the bowl when flushed to cover the complete bowl. This unit will have a lower water spot. What that means is the water in the bowl before flushing will not cover as much area as some toilets due to the low water consumption