Thanks!
While developing the game, I had an ideal tutorial in mind that would explain how time travel can be used to solve puzzles. But at the end of the day we barely even managed to add sounds and submit the game. As you can see, it literally says "1 second before the deadline" on this page...
Anyway, we've now added two mini-dialogues that help explain how items work with time travel and show how to solve the purple room button puzzle. There's also a full list of solutions on the game's page now, just in case you're interested
We'll check out your game soon and thanks again!