You don't need to have an anemone for them. I do enjoy watching mine however.
As for the topic of this thread, it's not really about how old the tank is, it's about how stable it is. I put a RBTA in my 29g after only 2 weeks. But I've been in the hobby for more than 10 years and it has a low bioload(only 2 clowns) in it. And that's it. So keeping it stable is not really hard. I had a plan, and I also had a backup plan with a LFS in case things went south.
Meanwhile I have a 180g tank that is about 1.5 years old, and I would maybe just now consider adding an anemone. I won't, because I would personally never put an anemone in a tank with other coral(most anyway). They move, kill things around them, and my 1 anemone has quickly become 3 anemones and all 3 are large and probably going to split again soon. The 180g has a very high bioload, it has a variety of coral that use elements, etc. Stability has taken time. You can't really say 6 months, 12 months or whatever. In that tank I'm not doing water changes and have to replenish elements and extract nutrients because it's a mixed reef. It's been quite a bit of trial and error and a few surprises. Not stable.
If there is any minimum time put on it, then it would be on the person rather than the tank. You need the experience to know when things are stable and that you're going to be able to keep them stable. And when you have that, you'll know then when it's ok to put in anemone or not.