A tithi is not a day. It is an arc, the interval in which the Moon gains twelve degrees of longitude on the Sun, and the civil day merely borrows its name. Shashthi occupies the arc from 60 to 72 degrees of that separation. Since lunar motion quickens and slackens across the month, the arc is crossed in as little as about nineteen hours or as much as about twenty six. The panchanga settles the mismatch by naming each civil day for the tithi in force at its sunrise. 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 Shashthi carries Kaulava, the third, and the second Taitila, the fourth. 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 30 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.