Export/importing posts – odd behavior with images and featured images

Hi, I exported posts with images, and when I import them into the wp website I’m working on – the instance on my local machine – the images for the posts come through and are set in the local database. That’s good and what I’d expect.

However, when I perform the same operation on another instance of the template on another server, the images reference the original websites instead of being set into that instance’s local database.

How do I fix this??

Also, sometimes the featured images are not set when they should be for many of the images on either of the aforementioned servers.