Automated update not working?

I’m trying to develop a module for a premium plugin to get automated updates from my own server through the “regular” update routine.

I have the system in place, it works.
The plugin is downloaded, unzipped, put in a folder.

But on the very last step where the original (old) version is deleted and the new version needs to be put in place the thing fails because the new folder is named “download.tmp” instead of the actual plugin name.

WordPress says the update was successful and is seemingly not aware of the issue.
Nothing in the logs but a bunch of errors of failed includes (because the folder name is wrong).

Has anyone heard of this before? Any thoughts?
Thanks in advance!