Those are used once you complete the area - you come back through there to get to the train. Easy to forget since it's a long time between seeing it twice.

Oh, I never realized I was going back through the same area as before! Thank you for clearing it up!

you can reach the secret hat room ONLY BEFORE you complete this area (Subway, Downtown, Campus, Inner City, Rain Night) and return to the train. After you get the component in this area and return, you will open the gate back to train and close the gate towards where you come here.
Here are positions to hidden hats room:
Subway: Under a laser where you need to use a period-strecthing gate to stop the laser shoot.
Downtown: Before you climb up of the sewer, there is a hidden room requiring a key. Use the key you obtain in downtown then go down to unlock the door towards the hidden hat room. Don't forget to take the extra key away to finish main line areas!
Campus: On the left hand of the man status(second board from main board towards finding the box), go down the stairs right beside the spring-board.
Inner City: On the first puzzle boards towards finding the key (southeast corner from main board), push the box stopping the bottom laser inside, then go down the hidden ladder.
Last Stop: after solving the first GREEN-PROTECTED puzzle, instead of going left and entering the elevator, go right then drop down the hidden ladder.