Island Sanctuary creature suggestion

Possible (minor?) spoiler about Island Sanctuaries ahead; you have been warned.

Seeing the rare/special creatures around the place is pretty cool, as is catching them. Could we have some in-game feedback that suggests when we'll see one again when it runs away, please? Something like "you suspect you won't see xyz again for abc days (Eorzea time)" or similar. I realise not putting anything about them in the help system is to let us enjoy the surprise and figure things out, but just a bit of a hint as to how they work would be really appreciated!

Loving the IS so far though, thank you!