The puzzles are quite well designed, and the game is overall pretty polished!
But I think the mixing of a puzzle game like this with a very strict time requirement just ends up making it very frustrating. Because with the time restriction, more than the player's actual decision making process, you're testing the reaction time. So even if you know how to solve the puzzle, the game won't let you solve it because you couldn't click on the piece the correct amount of times. So you actually just end up testing that gap between the player's mental abilities and their proficiency with the means of control. In my opinion these two clash against each other in this game, to the detriment of the puzzles. Then in the later puzzles, it turns into a pixel hunt where you're in a rush to make sure that the shapes that visually fit are colored correctly, and good luck if you're color blind. (Edit: Okay, the colors all have different values, so it's accessible I guess. But still :p)
TL;DR: Strict time requirements don't mesh too well with puzzle games. Maybe reward speed completion but don't require it. Keep in mind the target audience of a puzzle game.
Either that or just make the time limit longer :p
Aside from that wall of text, the track pieces overlapping on the same tile is a cool concept, and I liked the music too. Congrats!