Every turn, though given you aren't the first to wonder, I suspect the rules should be clearer.
Thanks, that's what I thought. This is how it said in the PnP rules, I guess you could interpret it both ways:
The Great Compromise segment is triggered once any player reaches 20 VP.
If the Chaos Rift is open, the Great Compromise takes place immediately after the Chaos Rift Struggle.
Once all players have received their VP award, the Compromise ends, the Judgeship ends, and play moves on to the Action phase.