Hendelbolaf |
Pathfinder Adventure Path Subscriber; Starfinder Charter Superscriber
My first response to the thread tittle would be in a bed, but now I see what you are asking.
It does not state it so I would assume it is more like a divine caster where they do not need any rest to regain spells or in this case extracts. Just pick a time and at that same time every day his extracts renew. OF course you will probably be under the same restriction that any slots used within the last eight hours are not available the following day when the rest renew.
I am not too versed on Alchemists so hopefully someone else has a more insightful answer for you.