Sorry for the long quote, but it will explain things better than I can. Its from Boeing's take on upsets and may help us understand why the climb happened. (Yes I know Airbus FBW is different from Boeing nevertheless a-lot of what is said reads accross)
3 Maneuvering Stability
Maneuvering stability, like static stability, is influenced by CG location. However, when the CG is aft and near the neutral point, then altitude also has a significant effect. Since air density has a notable impact on the damping moment of the horizontal tail, higher pitch rates will result for the same elevator deflections as altitude increases. From the flight crew's perspective, as altitude increases, a pull force will result in a larger change in pitch angle, which translates into an increasing angle of attack and g. While a well-designed flight control system, either mechanical or electronic, will reduce the variation of stick force with CG and altitude, it is very difficult to completely eliminate the variation due to design limitations.
For example, for the same control surface movement at constant airspeed, an airplane at 35,000 ft (10,670 m) experiences a higher pitch rate than an airplane at 5,000 ft (1,524 m) because there is less aerodynamic damping. The pitch rate is higher, but the resulting change in flight path is not. Therefore, the change in angle of attack is greater, creating more lift and more g. If the control system is designed to provide a fixed ratio of control column force to elevator deflection, it will take less column force to generate the same g as altitude increases.
This principle is the essence of high-altitude handling characteristics for RSS airplanes. Unless an RSS airplane has an augmentation system to compensate its maneuvering stability, lighter column forces are required for maneuvering at altitude. Longitudinal maneuvering requires a pitch rate, and the atmosphere provides pitch rate damping. As air density decreases, the pitch rate damping decreases, resulting in decreased maneuvering stability (see figure 2 and "Maneuvering Stability" below).
An additional effect is that for a given attitude change, the change in rate of climb is proportional to the true airspeed. Thus, for an attitude change for 500 ft per minute (fpm) at 290 knots indicated air speed (kias) at sea level, the same change in attitude at 290 kias (490 knots true air speed) at 35,000 ft would be almost 900 fpm. This characteristic is essentially true for small attitude changes, such as the kind used to hold altitude. It is also why smooth and small control inputs are required at high altitude, particularly when disconnecting the autopilot.