Quick test I did this evening: if I play against Magus, then I will face a timeout on his bot. If I swap positions, then it's my bot that is generating a timeout.
So it seems it is always second player that is impacted.
Checking my code, I can confirm that during first turn my bot is assessing he has 1 second left to answer then 100ms for next ones. Others bots facing the same problem could have implemented the same logic.
Then, if I reduce my first turn timeout to 95ms, then I do not face any more timeout...
Could the upgrade have affected that assumption in any way?