Perfect, thank you for your example.
The way this theme works is that if there is no Featured Image set, it takes the first image that was attached to the post and uses that one. That means that if you modify the post, or if you attach an image after the fact, it won't necessarily take the first image that it finds in the content of the post.
Try using Featured Images instead to always specifically define the image you want on the front page of your site, and I suspect that you'll have better results that way. Let me know if that works for you!