The algae cycles and the other microorganisms take time to level off... the biggest part is, your tank needs to find a balance with all elements coming in and out of the tank. I would say if you have a stable system with nitrates staying balanced and you don't have a bunch of algae blooms then your tank is stable... I would say minimum 6 months but only if you are lucky... most will take a year and some people never get a balanced schedule and are never fit for an anemone. Good documentation of what is happening in the tank along with weekly water tests will help you to determine when it is safe for an anemone.
I hope that answers your question and best of luck.
(these statements are a collection of what I know/believe they have not been verified by the elite members of AA