I apologize if I came across like I was scolding you. I got the two months from your profile information, but obviously what applied when you first registered on the site isn't the case now.
What I was trying to say, apparently a bit tactlessly, is that the anemone is moving because something in the tank is making it unhappy, and there could be a number of reasons for that.
If the water parameters are not just good, but stable and consistent, it's possible that your anemones are chemically competing with each other. You mentioned a GBTA that has split and a RBTA that is staying put; do you have any other anemones? Sometimes people keep different anemones successfully in the same system, but other times there's allelopathy, even if they're the same species. I think this is probably more likely to be a problem in small to medium-sized systems.
I recently had this problem when I tried to keep two different BTA morphs together (I have a 50G). The anemones became severely stressed not long after the addition of the new anemone. I didn't suspect allelopathy at first, but after I did a large water change and added a lot of new carbon, within about 48 hours the "original" resident anemone was back to normal. On the other hand, the smallest and newest one grew weaker even as the "original" got bigger and healthier, and eventually died (it had retreated into a place in the rocks where I couldn't reach it). (This is also the reason why I suspect it might have been allelopathy rather than tank conditions.)
Again, some people never run into this issue, but it wouldn't hurt to at least consider that possibility. If you're not running carbon in your system, I would add some, and see if that helps.
Good luck, and I hope my responses earlier didn't discourage you from asking for more help.