Thanks for your reply.
As far as I know (I am more of a beginner to be honest) I am not using a child-theme. I just installed SPUN and use it like this.
Okay, so I will use the archive.php and delete the category.php again.
Maybe the problem is something about how I display the posts in the loop itself.
I will try to recover the archive.php, add the query to change the order and then step by step change the way the loop prints out the posts.