The ability for the cross-tab to maintain the formatting when it is exported is not yet built into the Tableau Desktop product. More information on the idea can be found here: https://community.tableau.com/ideas/4501
Feel free to up-vote and share the idea!
Wow, I can't believe this is not something doable in Tableau. It seems like such a basic and obvious function to have. I think that Tableau drops the ball on small functionality like this way too often. Thanks for your help Patrick.