I'd like to offer an observation on this if I may.
I noticed the user said he annealed, and then is noticing rings on bullets. This is something I have helped customers with many times. After annealing, the oxidization which is noticeable as a gold sheen on the brass, is extremely tacky. If left untouched, it will really grab hold of those bullets. Both on the way in, and way out. Brass in this condition will cold-weld bullets faster than anything I've seen. It is pretty important to tumble that tacky sheen off before loading.
While measuring the neck diameter and then assigning a "neck tension" value is really the only thing within reach of most shooters, it is certainly not scientifically sound. The brass thickness, alloy composition, and surface finish have a huge impact on the actual force required to seat or release bullets.
I think you'll find that if you tumble that oxidized sheen off the brass or polish it out with a loose fitting or non-aggressive brush, that your issue will be resolved.
Having said that, as others have mentioned... I too have had many dies with seating stems which required polishing in order to remove the ring left on bullets. Typically a felt point with flitz held by hand while spinning the seating stem with a hand drill for a few minutes resolves the issue. When that doesn't work, the stem gets chucked into a lathe and more aggressive polishing is done. I always like polishing the insides of my dies for a better finish anyway, so it isn't too much trouble to me.