Is there an (un)official rule about twisting back a seat on broken bike for CitiBike or other shared bike programs?
This appears to be a widely-used, but unofficial way of communicating that the bike is broken and should not be ridden. See the Wired article that documents this trend: "Courteous Citi Bike Riders Are Alerting Others to Broken Rides" by Christina Boddington.

Also, on Twitter, you can find numerous examples (many of which were cited in the Wired post).