Hmm, given that it’s okay to send the visitor to an entirely different site, but you are trying to get it to show up as a page, I would suggest adding it to a menu.
You are probably already aware, but when you are modifying menus (Appearance > Menus) there is a box on the left side called “Custom Links,” which just like they sound, allow you to add something directly to the menu that can go anywhere. Add an entry using this that goes to the Tumblr blog and use that menu (whether it be primary or secondary) wherever you need to display the pages AND the Tumblr link. This avoids .htaccess conflicts and is the “natural” way to do things, but does restrict it to only being in menus.
Might be missing something here on how Tumblr recognizes the URL and the DNS issues, but from the WordPress side of things, that’s how I would go about it.