First, we have no evidence that the pusher fired for any reason, pure speculation.

The envelope of pusher actuation is dependent on the airplane's natural stall characteristics. In the CL600-series, there can be a rather abrupt roll off, in fact that is the case for many supercritical wings without slats. As the AOA increases, shock waves build and can suddenly cause a stall on one wing--especially on with even minor surface contamination or roughness. The certification standard is a normal pilot without unusual skills flying in accordance with the AFM. Mishandling a bounce is not anticipated.

GF