Just try to put a link of an image that is
yourdomain/images/xxx.jpg
JCE will replace this linke by a relative path like images/xxx.jpg
because "http;//yourdomain" is your domain url.
When working with multiple website and want to share some content between the website, it is important to ensure that you provide the full URL (include the http;//" to have the reference to this image in all circumstances.
This is not hosting dependend but related to extension like JCE that update the link that you provide to the image.
If you want to ensure of the link, you can disable JCE (or tinymce), to be able saving the full URL and avoid that the editor modify the link that you provide in the article (or Custom HTML module, ...)