Good game! The graphics are simple but pleasing -the characters models are cool- and the setting is well done. I like how everything has that old sepia tone to it in the "past" form. Music is a little repetitive, but I note that it seems to build as you go through the game. Medals are appreciated.
I really dig the concept, particularly how useful time-switching really was. Other than the agents, who are immune, swapping really does save you from dangers. I love how the technology changes between time zones. In the past, elevators (platforms) don't move yet and the teleporters are only half-built. The high-tech exit doors aren't installed yet. And the robots turning into mop buckets was quite possibly my favorite part of the game. I'm not sure you intended for this to happen, but the buckets seem to be "immoble" forms of the robots, because they still register the character. It was amusing how the buckets turned to face me when I walked by. Was that intentional, or just an oversight?
The only problems I have are things that have been mentioned below. After the first 10 levels I was thinking, "Oh, well, this is really just an interactive story." Thankfully, I hung on until the puzzles really started coming. On that note, the game isn't too tough. For the only levels I really got stuck on, it turned out I was just missing the solution. Once found, they were easy to implement.
The control are mostly solid, but the jumping is a little clunky. The only level that really gave me fits was 30. Unless I solved it wrong, there was quite of jumping over the enemies, and the hero's hit box seems a little wonky. It was difficult to guide him over the obstacles smoothly, and most of the time I got hit, I didn't think I had. 31 drove me a bit crazy, but again, it was easy once I realized that I was setting the level up wrong.
And, as mentioned below, the story never quite goes where the player expects. Again, the concept is very cool, but we're never really given any answers. The only great revelation is how the hat got into the house. It basically just the plot device to kick start the adventure.
Not a big deal, though... I got over it fast. The bottom line is that this is a creative and entertaining puzzle/platformer. Great work!