Matatirtha Aunsi falls on aunsi, the new moon, in the Nepali month of Baisakh. Baisakh opens the Bikram Sambat year and runs from roughly mid-April to mid-May, so the observance lands in late April or the first half of May depending on the year. It is not fixed to a Gregorian day and it has nothing to do with the second Sunday in May observed in the United States and elsewhere.
Because it is a new moon rather than a full moon, the date sits close to the dark end of the lunar cycle, and the earliest pilgrims come to the pond in genuine darkness. If you intend to be there, confirm the day against a Nepali calendar for the current Bikram Sambat year rather than any English-language listing, which frequently gets it wrong by a day.

