With Dipsy, you're meant to preemptively put on your mask before he storms the office. You see him walk towards you in the cameras, even has a few positions in the room right before the office. When he disappears from that camera, that means he's about to enter, put the mask then. You can technically still put on the mask around the same moment he opens the door, but any later and you're done for.
Tinky Winky on the other hand, I think he's really just meant to act as a timer of sorts to throw you off your loop if you forget about him, rather than forcing you to keep tabs on the office. That's why he pulls you away from the monitor and gives you ample time to put on the mask. You see his progress to make sure you can do all the stuff you need to before he interrupts you. It might make him way easier compared to the other tubbies, but to be fair, I can't imagine how tougher the game would be if you also needed to pay that much attention to him as well.