guada,
It doesn't matter who was the handling pilot at the time of the incident. But good cockpit management (CRM) suggests that the captain should manage the situation while the copilot handles the aircraft. This allows the captain to have time to think, generally oversee the whole operation, do the R/T and run the checklists.
From what I heard of the ATC tape that is what seems to have happened. As to who does what and when, that is solely up to the captain - who remains in control of the whole conduct of the flight.
It appears to have been a good job very well done. Not hero stuff, but good professional competence.