It seems every time we refresh our data, which adds a new month, the order of the manual sort gets mixed up.
I followed the below steps to make it work:
1) Remove the 'Calendar Month Date Start' from the filter shelf.
2) Right click on the Dimension column 'Calendar Month Date Start' and change the Default properties of Sort to Descending Sort order and Sort by to Data source order.
3) Then I applied the filter for 'Calendar Month Date Start' and chose #Individual Date. Selected the latest date on the top, as was populated from the data source and chose OK.
4) Again, went back to the dimension 'Calendar Month Date Start', right clicked on it and selected Date format. There, I chose 'March 2001' from the list (you may select any format you like for view) and selected OK. There you go, the filter is now sorted in the chronological order (descending).
5) I have ignored the 'Formatted Name' column being a Calculated field and used the date format to Sort the field.
Oh my goodness, Souvik, YOU ARE MAGIC!
Thanks for your help!