RAW: "You can only spend XP during a Quarter Day when you REST or SLEEP." (See page 39 and following.)
This may be a translation or wording error, or just chalk it up to the strangeness of English. "When" can mean "after" or "during" as it is written here. The text goes on to explain various restrictions or exceptions to this statement, but does not clarify this problem of interpretation.
While I think you can make cogent arguments for either interpretation (and we can always play it as we want), I'd love to know the original intent. is it:
(A) It seems like you can increase skills and talents during sleep, that correct? (Ex for the exceptions re: first rank, magic, etc.)
OR
(B) Is this saying you must have had rest or sleep in order to train (spend XP)? If this is the case does all training take 1/4 of a day?