You have to have the trailing slash in your url if you’re using the specific URL option:
mywebsite.com won’t work
mywebsite.com/ will work
It’s likely because the videos are in iframes, and wordpress removes them on import for security. I made a blog post on how to fix this:
http://www.brianshaffer.com/how-to-fix-wordpress-to-tumblr-video-importing/
