By all means do ask - it's not often that people are interested in this stuff! (Plus, I'm doing this in part to learn more about Geostatistics; interpreting and discussing results is a big part of that.)
The measurement of hot/coolness that results from the analysis (so, the Gi* statistic) corresponds to positive/negative values with negative numbers representing coolness. I calculated this statistic twice, once for diversity changes per county and once for diversity changes per county. The above map shows, like you interpreted correctly, places that are hot at both phenomena or cold at both phenomena.
As a baseline, I compared the current election results to the last time a GOP candidate moved. I think it paints a more accurate picture of whether the nation moved to the right or not than comparisons with Romney or McCain. If I had data for all elections on a county level I might've done a trend analysis on a per county basis... but for some stupid reason election data is not a public good and [the source everyone seems to be using](uselectionatlas.org/BOTTOM/store_data.php) asks $60 per election. I am considering doing a more rigorous analysis that incorporates income and status of minorities, but I don't know where to find the time to do that just yet.