I agree that the wording is quite confusing, but you should be able to understand each label just by observing how things work.
You can place a companion wherever you want in the pot.
When a companion is anywhere in the pot and the corresponding set is available:
- if you already collected the gift you will see the message "Already settled in" and the character will stay where you placed them
- if you never collected the gift and no one else is waiting at the set, the character will move there and wait for you. In this case you see the message "Gift event has yet to be completed". After you collect the gift they will return to their place.
- if you never collected the gift but someone else is already waiting at the set, you get a message "Please collect the gifts you currently have". They will try to move to the set as soon as it becomes free.
When multiple characters are available for a set, only one will go there and the other will wait for the set to "free-up". I don't know how the priority here works, I assume it is either character ID or join date.
When the set is free you can also invite a character there to listen to the dialogue again.
NOTE: If you place a set and then place the character nearby manually things may get confusing because it may look like TWO characters are there but that is not the case (ex: built a Cottage Kitchen and put Xianling there, then add Mona somewhere else , Mona will move there too if you already got Xiangling gift since the set is "free").