at the precise hour (expected, predicted, anticipated etc): right (precisely) at the appointed (expected etc) time (hour)
(predict (prophesy etc) sth. ) (right) to the very hour(in limited contexts) right on time.
"...Я тебе рассказывала, кажется, как Кирюша день в день, час в час предсказал покойнику папеньке его кончину» (Толстой 2). UI believe I told you how Kiryusha prophesied the end of poor Papa, right to the very day and hour" (2b).