If a person is charged with Trespassing in Arizona, do they have to be arrested and sited before actually being charged??

Short answer: No.  If it is a misdemeanor trespass, the officer can charge you by citation, or he can submit his report to the city or county attorney who can charge you by "long-form" complaint. Typically, you would receive the complaint in the mail with a summons to appear in court.  There is no requirement that you be cited and arrested in order to be charged.