While the agreement's wording is not a model of clarity, I'll excerpt the relevant portion for you below to draw your own conclusions about whether it grants the US authority to prosecute US military personnel, US civilian employees, and US government contractor personnel. The agreement uses the phrases US civilian personnel and contractor personnel elsewhere, so that may inform your interpretation of the term "US personnel." Diplomatic Note No. 202:
The Government of Afghanistan recognizes the particular importance of disciplinary control by United States military authorities over United States personnel and, therefore, Afghanistan authorizes the United States Government to exercise criminal jurisdiction over United States personnel. The Government of Afghanistan and the Government of the United States of America confirm that such personnel may not be surrendered to, or otherwise transferred to, the custody of an international tribunal or any other entity or state without the express consent of the Government of the United States.