Tactics trainer gone wrong?? Or am I missing something?

The previous position was Bxc4 and now black to move. I first played Bxf3 because if I eat the knight, I gain a tempo on the queen and white doesnt have time to move the white tile bishop. Instead the trainer said incorrect( look at my tactics rating, it went down)so I played bxc3. I believe Bxf3 is better or am I wrong?

You got a free bishop,why would you not take it? and you don't gain tempo on Bxf6 you lose material..

You are very wrong. If you play Bxf3 white will play Qxf3. Now you cannot take the bishop. Because if you play bxc4 white has Qxa8. The queen on f3 is attacking the rook on a8. Not only that but the queen is threatening mate on f7. So you cannot defend the rook. You have to play bxc4 and white will play Qxa8. Now you have lost rook for bishop. Had you simply taken the bishop in the first place you would have been a piece up. 

The problem here is that you have heard and seen a out the idea of tempo. It's good that you were considering an in-between move such as Bxf3. As you say, black does not have time to immediately save the bishop. So it was worth considering. However, you have to look deeper. In the end it turns out that Bxf3 loses a tempo for you not wins one.