This legend could be the source of many references in the anime Love Hina as well.
Certainly the character names are no coincidence; the main character's name is Urashima Keitaro, and (for a large portion of the series), one of his love interests is named Otohime Mutsumi. There is also a great deal of turtle imagery in the series.
Not too long after Mutsumi's introduction, she does in fact give Keitaro a box, though she says to "open it later" rather than never opening it at all. Rather than containing white smoke, however, it contains Tama-chan, the Requisite Cute Animal of the series (a turtle, of course).