I might be a little slow but I'm not sure what the problem is. EST and CDT are the same time so the axis should be the same. It might be better to not include the standard v daylight in the param and adjust for it within the axis. The date is 9/30 so I would use *DT by default.
Maybe create a calculation to offset [Adjusted Date Time] by an hour depending on whether the date portion falls in Standard or Daylight time and the timezone selected isn't GMT.
DATEADD('hour',IF [Time Zone (copy)]!=0
AND [Created At Date Time]>=MAKEDATE(YEAR([Created At Date Time]),3,13)
AND [Created At Date Time]<=MAKEDATE(YEAR([Created At Date Time]),11,6) THEN 1 ELSE 0 END,DATEADD('hour',[Time Zone (copy)],[Created At Date Time]))
Looking forward to seeing what you came up with.
I've attached a modded workbook to demonstrate my idea but all the data falls within daylight savings time so not all cases will be tested but it seems to work fine for the data we have.
I'm only a couple months into using Tableau, so excuse any naivety...
As for why your problem exists, the Daylight Savings Time values have a value of 1 less than their standard counterparts. This explains why CDT is equivalent to EST, MDT to CST, and PDT is equivalent to MST. In the US we observe DST from the second Sunday in March to the first Sunday in November. Given the workbook you provided, I only see one date (September 30, 2015) which clearly fits within the confines of DST. To verify DST status in this case, this would be enough of a test:
IF DATEPART('month', today() ) >= 3 AND DATEPART('month', today() ) <= 11
The challenge as I see it is how to limit the parameter choices based on a calculation result (e.g. 'True' might only let you choose Daylight Time zones, 'False' might only let you choose Standard Time zones). For this, I'm not sure how I would proceed. Fun mental exercise though!
you're absolutely correct to not see the problem. The axis will not change, the new workbook has the title that should change and does not when changing from EST to CDT.