because they are extremely hard to care for, they need good flow (not sure on yours), high lighting (not enough in those cubes) and excellent water conditions. Even in a much larger tank, with much better lighting, I wouldn't add one until the tank was 6 months or more old. The older a tank gets, the more mature the rock and bacterial colonies become and the more stable the water conditions are. A new nano is about as unstable as a tank can be. What exactly did the guys the the shop test for? I'm guessing it was just amonia / nitrite, no iodine or any trace elements the anemone needs...
In the entire time I've been keeping a nano tank, in all the reading i've done, the only anemones which I know of or have read any accounts of doing well in a nano are aiptasia...