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Not all spontaneous casters need rest, oracles for example do not.
Time of Day: A divine spellcaster chooses and prepares spells ahead of time, but unlike a wizard, does not require a period of rest to prepare spells. Instead, the character chooses a particular time of day to pray and receive spells. The time is usually associated with some daily event. If some event prevents a character from praying at the proper time, she must do so as soon as possible. If the character does not stop to pray for spells at the first opportunity, she must wait until the next day to prepare spells.
Oracles have the following language
Unlike a cleric, an oracle need not prepare her spells in advance. She can cast any spell she knows at any time, assuming she has not yet used up her spells per day for that spell level. Oracles do not need to provide a divine focus to cast spells that list divine focus (DF) as part of the components.
So beside what is stated above they should follow the rules for divine casters as far as time of day and no rest required.
What reference is there for spontaneous always requiring rest?
It still is 'Spells per day':
A psychic can cast only a certain number of spells of each spell level per day. Her base daily spell allotment is given on Table 1–7: Psychic. In addition, she receives bonus spells per day if she has a high Intelligence score (see Table 1–3 on page 17 of the Pathfinder RPG Core Rulebook).
A psychic need not prepare her spells in advance. She can cast any psychic spell she knows at any time, assuming she has not yet used up her allotment of spells per day for the spell’s level.
There's no time given, and it doesn't seem to require rest, but it still is an amount of spells per day.Seeing as most races need 8 hours of rest per day anyway, it would make sense to replenish the spells at that time.
Note that the psychic spells lack the notion of a recent casting limit.