They are not made visible while you are doing rated problems. They would give you too big of a hint.
Some people want them visible, so that they can pick and choose thematic problems. Solving, for example, a whole bunch of fork problems in a row, etc.
There are other threads on this.
http://www.chess.com/forum/view/suggestions/improving-learning-value-of-tags-in-tactics-trainer
I searched FAQs and did a thread/forum search, but could not find an answer. In the Tactics Trainer settings I have the "visible tags" checked. The tags are not visible until completion of the puzzle, though. Is this the way it is to work, or are tags supposed to be visible before you start the exercise? Thanks. If they are supposed to be visible before the exercise, can someone tell me how to activate that feature? Thanks.