See the attached. There were two issues, one was that the table calc was set to Compute Using Table (Across). That setting is completely dependent on the arrangement of pills in the view, so when you moved to the map the results would change. The Compute Using that is needed is Order Date.
The second issue was with the filtering. The basic filters in Tableau are processed within the data source, so they limit how much data Tableau gets. For the calculation you want, we need a filter based on a table calculation, which can be as simple as LOOKUP(ATTR([field]),0). I used a variation of this for the filter. Filters based on table calcs are processed after the data is returned to Tableau, so the Q over Q calc can work.
Note that not every state has data for every quarter, so the LOOKUP() doesn't always return a quarter, that's why there's an empty radio button on the Quarter of Order Date filter. That's also why some states (like Wyoming and South Dakota in 2012 Q4) don't show any coloration.
Thank you so much for your insights, and for an answer to my problem!
The filter workaround worked just like you said and provided a great solution to this problem.
One thing to note, the example you posted needed a little tweaking. I needed to change it from using the order date field to using the order date field that I created that represented the date in quarters. I've attached the tweaked version so that others might benefit from your clever workaround.
Thanks for taking time out of your day to help me out. People like you help make Tableau great!