It will be interesting to discover if he did the shut down drills on the failed engine or just assumed it had turned itself off and didn't need further attention.
A pretty standard action post any engine malfunction would be to check for dangerous indications.
While I agree Crab there was not a lot of time. My company requires engine shut downs to be done from ECL(believe it or not Fire drills too……)Works great for a chip light perhaps not for an uncontained engine failure with fire.
“IF” you follow the process it takes forever.