The monsoon season as defined by the NWS began June 15th and runs through Sept. 30th. These dates were set by the NWS in 2008 in order to help the media effectively communicate that thunderstorms are possible during this time frame. For many years the criteria of 3 consecutive days of a 55 degree average dew point in Phoenix (54 in Tucson) was used to declare the beginning of the season. Flagstaff never set criteria and used Phoenix as a guideline. In Phoenix, the average start date was July 7 and the earliest onset occurred on June 17, 2000.
The National Weather Service in Flagstaff has compiled 2014 weather statistics for much of northern Arizona and the numbers aren't very good. Flagstaff recorded it 3rd warmest year since 1898 while Prescott recorded it's 1st warmest since 1948. It was also the 1st warmest year recorded for Winslow and 2nd warmest in Page. Flagstaff ended up with 20.67" of precipitation which is 95% of the yearly average. This is largely due to a wet monsoon.