I tested this a bit further on a clean install and I am not able to reproduce the issue. For example, use this link to login: hidden link
Go to WPML -> Translation Management -> Jobs and filter by In Progress and Translation ready to download. I get the results for In Progress, and there are no translations that are ready to download. Feel free to test around on this sandbox site and if you are able to reproduce the issue please let me know.
If you aren ot able to reproduce but it is still happening on your site with the latest versions, then it's possible there is some conflict with another plugin and we should test in minimal settings.