IMO timing tactics is ridiculous. People would be compelled to try what looks good without figuring it out... it's practicing sloppiness. In my opinion the only way to do tactics, any tactics, is to solve it 100% before you make the first move. If the 2nd move surprises you, that's fine, solve it 100% from that point. That's how you get better at tactics.
I suppose timed tactics could help something? Probably only quickening the patterns you already know. I can understand why if quick tactics were the only tactics you do you'd see very little improvement.
I only set Tatics Trainer to rated (timed) when I want to get an idea of how much I have improved. So, I will do 25-50 rated puzzles and then STOP, record my rating, and then RESET my tactics trainer history. Then I will go back to doing unrated puzzles and solve them at 100%, no mistakes, taking as much time as needed per puzzle.
I will spend 99% of my tactics training sessions on unrated puzzles, both here and at Chess Tempo, and ONLY do rated puzzles every other month, once, as a test, to check my progress.
So, I suggest seeing the unrated puzzles as practice, and the rated puzzles as the test. In school, didn't you do far more homework (practice) than quizes and tests? See tactics traing as going back to school.
Last, I have improved a lot more in tactics by doing it the old fashioned way, without a computer. I go through ONE puzzle book until it's all worn out, and the basic patterns are burned deeply into my brain, and then I pick up another tactics puzzle book. Rinse and repeat. I don't think there is any good substitute for high quality tactics puzzle books. Dan Heisman talks about the problem with doing 950-1200 rated puzzles on chess web sites. It's not as efficient as getting a few really good tactics books that cover the basic patterns we NEED to know.
One important thing is you have to train recognizing patterns, with a tactic book for example : fork, skewer, mating net, discovery attack, X-ray, pins...