You’re right, that’s an edge case I didn’t account for. Normally an open tab doesn’t generate Time Points because the game continues running in the background rather than pausing like most browser games.
However, if it reaches a major decision and has to stop for player input, then leaving it open can currently leave you with neither progression nor Time Points. That isn’t a good outcome. I’m going to look at having time spent waiting at a blocking decision count toward Time Points, so leaving the game open doesn’t actively disadvantage you.