Lyman;
As has been reviewed on numerous occasions, the SOPs to deal with an abnormality come under the heading (as you probably know) of aviate, navigate, communicate then deal with the abnormality or emergency. Control of the aircraft is first assured, then ensure terrain clearances, then communicate internally (announcing the emergency/abnormality and calling for the drill or checklist, then when all is done, communicate with ATC then the flight attendants/passengers.
Except for the rejected takeoff and TCAS/GPWS/Stall warnings, no emergency and certainly no abnormality (which this was), requires immediate action and never without crew coordination.
In the RTO for example, crew coordination may be just the announcement "Reject!", followed by the simultaneous closing of thrust levers, selection of reverse, monitoring/applying full brakes and ensuring ground spoilers are up. At a minimum, announcing the drill or checklist ensures awareness and subsequent coordination and appropriate action.
In abnormalities, on the Airbus the PM calls the ECAM name of the abnormality, the PF calls for "ECAM Actions" and the PM reads (silently) and carries out the ECAM checklist items, confirming any non-reversible actions with the other crew member before actioning them. Then the STATUS page is then checked for system/aircraft unserviceablilities and possible performance considerations.
Where/when required either by the ECAM or company SOPs, the QRH is then brought out for further responses to the abnormal. The entire process including high levels of CRM is heavily emphasized in all initial and recurrent simulator sessions, check flights and in the aircraft manuals.
It is against all this that the response of both the PF and PM is astonishing and incomprehensible even given cockpit gradient and lack of command assignment and consequent assessment and decision-making issues. It may be unfair to observe (because I wasn't there, not because it isn't reasonable to expect), but upon initial pitch-up without announcement from the PF which is non-standard and highly irregular behaviour I would have expected the PM to announce, "I have control", level the airplane, call for the UAS checklist and sort it out with the captain later, on the ground.