The monsoon has begun in Tucson:
Source.This NOAA graph shows dewpoint, a measure of humidity. The blue line for this year is above the average, red line, and passed the 54 degree cutoff in early July. The monsoon is somewhat arbitrarily defined as any period of three or more consecutive days when the dewpoint is 54 degrees or above. In Tucson this kind of moisture only happens during the monsoon, when the wet tropical air pushes north. More info.
The rainfall so far has been above average as well. This graph does a good job of showing the variability of rainfall between cities that are less than 100 miles apart. When it comes from isolated thunderstorms, sometimes they hit you, sometimes they miss you.
The rain has not yet helped out New Mexico and Texas (source), but the climate forecast is for New Mexico to get a good amount of moisture over the next month: