That makes sense! I think it's impressive enough to make the narrative as logical as it is when time travel is involved.
To clarify, I "won" with: Code1: "Both are same" Code2: "Both are same" Code3 "Player I same" which probably shouldn't have worked.
A few other minor things:
At the very beginning, you have a conversation with Pigeon that goes Pigeon - "Yes, since we won't have time to deliberate. It's a very structured conversation." Player - "They?"
The player's response here doesn't make sense, since there is no "they" to ask about. Maybe the player could say "Deliberate what?" or "We?"
Perhaps you can bold the parts of dialogue when the characters tell you what the code should be used for, for example:
Pigeon - Using the code, you need to let me know how you feel.
Pleasance - Use the code to tell me anything Pigeon tells you about the vote.
This may be easier for players, and would also be nice to show the players response to reference when scrolling up through past dialogue (for example, if we agreed on "use the first letters" or "use the last letters")
The circles at the bottom could be more intuitive too, perhaps by giving them all days of the week, and leaving the past meetings as "?" before you unlock them. So it would look like (from left to right)
Monday: "?" -> changes to "Secret meeting with Pigeon"
Tuesday: "?" -> changes to "Secret meeting with "Pleasance"
Wednesday: Meeting of the delegates
Thursday : VOTING DAY