Did NASA/JPL get "waning" and "waxing" backwards in this video?
I think they did make a mistake.  The moon waxes after a new moon and wanes before a new moon. To wax means to grow bigger or stronger (and is cognate with "waist"!). To wane means to become smaller or weaker (cognate with "waste" and "vaccum").

The moon that sets shortly after sunset in the evening is a waxing moon. The moon that rises shortly before sunrise in the morning is a waning moon.