Sorry, I forgot about this topic.
I only just today got around to finding the fix - turns out that the Elegant Themes theme I was using for WordPress had a bit of code in it that altered the query in such a way that only custom post types were affected in this way. So it's not a problem of this plugin, it's Elegant Themes that's messing up, I think.
I believe the code was intended to limit the amount of posts displayed on the webpage, but instead altered the maximum amount of posts shown on custom post types created via Types.
In the Elegant Themes 'Theme options' screen there is an option called "Number of Posts displayed on Archive pages" that can be set. An unfortunate side-effect is that it forces the dashboard to only show that amount of posts - but ONLY on the custom post types, the normal posts and pages are fine.
Simple solution: set that number and the dashboard will follow.