This objective seem to be quite glitchy. Often it doesn't work, for example if I assign dweller having highest stat S to power room - nothing. I assing another dweller with high strenght to power room and game counted it instead.
You must assign dwellers who are not in the righ room yet. Strenght center is focused on strength and so is power room so it does not work. I usually use dwellers that train some stat that is not their highest at that time or do another objectives and skip this one the next day. (The same with bald dwellers and pregnant/baby ones, when i am not ready for deathclaws yet).
This objective is nearly impossible to complete because I have all my dwellers in right rooms already and game seems to remember where dwellers were previously so I can't do any "assign S-guy from power room to warehouse and back"-tricks either. Only thing I can do is assign returning explorers to warehouse (high E stat). Simply not worth the hassle unless rewarded with a luchbox...