Hold-up, that's not supposed to happen!
When you say "starting with another playthrough", you do mean with the Start button, right? Or did you try the Scene select button? Or the Dialogue-Rollback feature? Did you try the Data reset in Preferences?
And so when you get to the timer sequence, you can't interact with, like, the portrait next to the bed or with the fridge?
This never happened to me, so I would need to check it for myself. As far as I know there should be no reason for this to happen. What says you've interacted with those is not supposed to persist between playthrough.
Would you be able to join the Discord server to share more informations about that in the Feedback channel? If it's as you say, it should go into my "need to investigate" pile.