I understand your question, but you may get something wrong. There is no pre-multiplication of alpha when you export PNG. Here is the comparison of the exported result:
The left side is the exported PNG and the right side is the exported PNG atlas texture using Premultiply alpha
option. You can see the difference by the color around the muzzle flash.
Therefore, I guess there is another cause for the black borders. Could you send your Spine project via email? : contact@esotericsoftware.com
Please write the URL of this post in the body of the email. We will investigate it and respond to you later.