The answer from the Mathworks is not good enough !? There's quite detailed description of the workflow available at [http://se.mathworks.com/help/gads/how-globalsearch-and-multistart-work.html]. If there is an error maybe you should contact the guys at Mathworks directly...
When you run a GlobalSearch object, the algorithm performs the following steps:
Run fmincon from x0
Generate Trial Points
Obtain Stage 1 Start Point, Run
Initialize Basins, Counters, Threshold
Begin Main Loop
Examine Stage 2 Trial Point to See if fmincon Runs