Global 6000 Captain reported the First Officer temporarily lost situational awareness and control of the aircraft after mistakenly thinking the autopilot was engaged.

Narrative

As a crew we discussed the prescribed noise abatement procedure out of the airport. I was the pilot monitoring. First Officer sitting in the right seat; took off. After crossing 3000 feet; while still hand flying; pilot flying turned left to the north. While I was communicating with ATC; the Pilot Flying; while still hand flying; was inputting inputs into the autopilot panel. While intercepting the airway; the flying pilot banked the airplane between 40 and 45 degrees bank left; and also pitched the nose down; resulting in descent of 2500 ft./min. I brought it to the attention of Pilot Flying who was confused and stated 'what is it doing now; and why?' The Pilot Flying had lost situational awareness. After leveling the wings and bringing the airplane to a climbing altitude; the autopilot was immediately engaged. The pilot flying indicated that they thought the auto pilot was engaged due to the high load forces on the flight controls. The Pilot Flying indicated that she had become overly reliant on the automation; and had forgotten how heavy the flight controls felt; thus the reason they thought the airplane autopilot was engaged. This particular tour has shown several weaknesses of this crew member. A lack in basic airmanship; procedural policies; and situational awareness were demonstrated in this week. I am not sure if this aircraft or mission is a level where said crewmember should be operating.