What determines when the Flores de Mayo and the Santacruzan festival will occur each year? As Wikipedia says:


  Flores de Mayo (Spanish for "Flowers of May") is a Catholic and
  Aglipayan festival held in the Philippines in the month of May...The
  Santacruzan is the pageant on the last day of Flores de Mayo, held in
  honour of Helena of Constantinople (known as Reyna Elena) and
  Constantine the Great finding the True Cross in Jerusalem.


The Santacruzan appears to always be held on a Sunday in May (a parade goes by my apartment in New York City). But what determines the dates of the Flores de Mayo (including determining what Sunday the Santacruzan will be celebrated)? One data point: the day for 2014 seems to be today (May 18).
According to a page on the Northern Illinois University site, the festival concludes a Novena (nine days) of prayer.

The festivity commemorates the search of the Holy Cross by Queen Helena (Reina Elena) and her son, the newly converted emperor Constantine. After the Holy Cross was found in Jerusalem and brought back to rome, there was a joyful celebration for thanksgiving.
Nine days of prayer (a novena) in honor of the Holy Cross precedes the Flores de Mayo or Santacruzan. This festival was introduced by the Spaniards in the Philippines and has since become part of Filipino traditions identified with youth, love and romance.

The feast of the Finding of the True Cross as introduced by the Spanish would have been celebrated on May 3, which is when it appeared in the Galician calendar. The festival was suppressed when it was combined with the Roman celebration of the Triumph of the Cross (September 14) in Pope St John XXIII's New Calendar of 1960.
As the main procession in New York always occurs on a Sunday, the Novena of prayer would start nine or ten days prior to that — depending on whether the procession is on the last day of the novena or the day following it, celebrating its completion. This year, it fell on May 18; thus the novena would have started on either Friday 9 May or Saturday 10 May.
I would surmise that the novena starts on the Friday or Saturday following May 3, which would fix the final festival on the third Sunday in May.