The spatial–temporal discharge behavior of an AC argon plasma jet tilted at non-perpendicular incidence angles (60°, 45°, and 30°) interacting with an ungrounded metal, water, and glass plate placed on the jet propagation track was studied by the fast-imaging technique. The conductivity of surface and incidence angles plays an essential role in the discharge current and dynamic process of the plasma jet. The nearly consistent time delay between subsequent breakdowns occurred four times for metal and two times for glass treatments. The mean luminous intensity of the plasma in one discharge cycle at the discharge area between ground electrode and target surface region for the water and glass case decreased by 39.5% and 20.5% when the incidence angle decreased from 60° to 30°, respectively. In particular, the incidence angle and gas flow rate notably impacted the spatial extension behavior created on the glass surface but had no significant difference in discharge characteristic of plasma jet with metal case. In addition, two equivalent circuit models were developed based on the simulation of the micro-discharges and the geometry of the “plasma jet–substrate” system, respectively. These results will obtain further insight into the underlying mechanisms of plasma-target interaction and facilitate the designing of appropriate jet for environmental and biomedical applications.