cf. Zenobius 3.79; Hesychius epsilon3383; Photius, Lexicon epsilon1039.
Such a stipulation is otherwise unattested. (Photius says the reason for it had been given in Callimachus' Aitia.) For the preposition e)nto/s in this sense see LSJ s.v.
1sc. day of the month: explicit in Hesychius, Zenobius and Photius. (Contrast e.g. Plutarch, Marius 17.11, where e)nto\s e)bdo/mhs h(me/ras refers to the tribune Aulus Pompeius dying 'within a week'.)