Shutting down and rejoining the server causes a variety of issues with the Terrarium while it's active, depending on different times of day. These were done on a solo world:
After beginning the fight at night, quitting the server at the break of dawn canceled the Twins despawning, making it possible to fight and kill them during the day. This also caused them to never enter their second phase, and not drop the shield item.
Without ever starting the fight previously, quitting and rejoining during daytime while the Terrarium was active (floating) caused it to start its beam animation. This did not spawn the Eye of Terror, even after waiting until night, and it could not be picked up or deactivated.
Quitting during daytime in the same way, this time with the corrupted Terrarium, caused the Twins' fight to start in the morning and progress as normal. No idea why the same thing didn't happen with the regular Eye.
Save and quit at any time while the Terrarium is active, either floating or during the beam animation (solo world, early autumn, no mods)