Same here, always have to refine myself...thought the membership had auto refine.
Now that you mention it... I subbed at the first of this month but I'm still having to refine mine manually. Hadn't really hit me as I was used to doing it that way but according to the membership listing on the site it's supposed to be automatic now... hmmmmm...
The auto refinement doesn't happen if you refine manually. I log in everyday, and I never manually refine. There seems to be a set time when the refining is set to happen. For me, it's in the evening some time. When I log in, I immediately get a message "You refined xxxx dilithium". This only happens once per day. If I earn more dilithium, log out and log back in, there is no auto refinement even if I didn't reach the 8K cap previously. The next auto-refine doesn't happen until I log back in the next day. It's actually a great way to keep track of how much dilithium I have earned in a single day. I actually don't have a backlog of unrefined ore (or at least very little). I think the most I ever had is 10K (I actually earn a lot more in total, but it's just spread across 6 characters, so I rarely reach my refinement cap on any one toon).
So, to test the autorefinement, stop manually refining. The system should 'catch up' after a day or so.