Reckoning a tithi means measuring elongation, the angular distance of the Moon from the Sun, and cutting that circle into thirty equal twelve degree arcs. Ashtami occupies the arc from 84 to 96 degrees of that separation. The Moon does not move at a fixed rate, and the same twelve degrees may take a little over nineteen hours near perigee or close to twenty six near apogee. A calendar has to name whole days, so the rule is that whichever tithi is current at sunrise gives the day its name. A tithi shorter than the interval between two sunrises can therefore be skipped entirely, which the tradition calls a kshaya tithi, and one longer than that interval can carry its name over two civil days, an adhika or vriddhi tithi. Both occur in the ordinary course of a year, and both are why an observance can appear on two dates in the same almanac.
Each tithi is halved again, and each half carries a karana, so the first half of Ashtami carries Vishti, the karana also called Bhadra, and the second Bava, first of the seven movable karanas. Vishti is the one karana the muhurta literature marks as unfit for beginnings, and its presence in the first half is why this tithi is read with more care than its neighbours. Seven of the eleven karanas repeat, cycling eight times through the month, while four are fixed to particular half tithis at the month's opening and close.
The Moon is waxing through this arc, setting later each evening and carrying about 50 per cent of the disc lit. That figure is a consequence of the definition rather than an observation added to it: elongation fixes the phase, so naming the tithi already names how much of the disc is lit.