Really getting into the nitty-gritty here. If an entity migrates to an inactive chunk, I keep the entity "on hold" and add a "chunk set mutation" to the active chunk set so that the set is expanded in the next tick. The processing thread for this newly added chunk sees that no data exists yet and synchronizes the state from the backend during the subsequent tick. On this tick the entity gets added to the new chunk write state and disappears quietly from the old chunk in the next tick since it isn't "on hold" or copied anymore.

As for the processing per tick: the entire active chunk set gets semi-randomly processed by threads. You'd be absolutely right that the order of operations isn't always deterministic. An entity not being processed for a tick doesn't happen since the old chunk will still process entities that are "on hold", but only perform a subset of operations. Double-processing does occur and this is sometimes visible while playing with a chat message being duplicated. This happens pretty rarely and I took care to make sure occasional double-processing doesn't interfere with gameplay mechanics.

As for synchronization: yes, each tick all processing threads join together and the server performs minor central processing and scheduling. Then the next tick begins and all threads are started again.