There seems to be an issue with TubePress under WP 3.9.2 when running on a WP network with a mapped domain using the http://wordpress.org...domain-mapping/ plugin. I only tested this with a network of subdomains, but I assume the problem exists with subfolders as well.
With that plugin, the siteurl in the site options stays as a subdomain of the main site. The domain mapping plugin handles adjusting this to its mapped value.
When TubePress sets the URL for the wp-content/tubepress-content folder, it appears to be building the URL by using the siteurl, which produces a URL using the subdomain (undesirable) rather than the mapped domain (desirable). See the source of this site http://www.upf.tv/ as an example. Just do a search for tubepress-content and you'll see its URL is set to the subdomain rather than the mapped domain.
This is fixable by manually editing the siteurl & home values in the options table for the site, but that's something that the plugin authors don't recommend.
Domain mapping is probably going to get rolled into core by about WP 4.4, but it would be great if TubePress fixed this.