I would like to think that any pilot worth their salt would immediately grab the controls to level the aircraft. As you say, this should be instinctive and automatic - no thinking required.
I wonder if PF got too closely involved with avoiding CBs and just did not notice the increasing thrust lever and N1 split and the increasing bank on the yokes? If both PF and PM were concentrating on the weather radar and looking out to avoid and find a path between CBs; maybe the increasing asymmetric situation was simply not noticed. Then with no warning, the auto-pilot suddenly drops out and the aircraft rapidly banks over..............