Happens only when you're logged in, as the study take will consume curiosities only with the character being active (retroactively for the time it was logged out).
To clarify what Granger said at the end: Any curiosities that "finish" while you're offline are actually just stored up and pop the moment you log in. That's when the authority generation happens as a result.
Lucky: haven is so quirky Lucky: can be so ugly, can be so heartwarming Sevenless: it is life