tactics

Never seen that happen.

Wierd, I've never seen that before. Did you report this? 

Basically you took too long, which means you can go as low as 20% score.

If the puzzle is the same rating as you, you will need 50% to not lose points.

I don't think I've seen that, but I may just be forgetting one of many problems where the Tactics Trainer behaved irrationally.  It has penalized me many points for missing the 4th move of a combination - yet one that still won - while awarding me just one point for taking more than the "standard" 7 seconds for finding a tricky 3-move combination.  Then it awards me a ton for seeing an easy, forced-opponent-move, mate in 2 that involved some well-known tactic.

Here's how it did work. There was talk of changes so not sure how much is still correct.

Firstly the total clock is 2x average time. Take longer than that and your score is capped at 20%. If you take the average time I believe you get 80% but not completely sure on that number. This score is then multiplied by the percentage of the problem you got correct. So 1 out of 2 moves in the average time will get you 40%.

The change your percentage score makes to your rating depends on your rating relative to the problems rating. So 50% on a tactic at your rating and your rating won't change. But for a lower rated problem you will lose points, or gain for a higher rate problem. The exact formulas for this depend on a rating deviation similar to your chess rating so your rating will change more quickly at the start.

The problem rating will have the opposite change but not necessarily by the same value.

I would be interested in seeing the tactic that the OP is referring to.  This is site i not my major tactic site so i don't know if/what has been changed.