I would have expected the FE to simultaneously advise the Captn of the indications, and be slowly retarding the power, I say slowly because of the phase of flight they were in, as well as selecting maximum power on the other three engines.(At that stage I expect that climb power would be set!)
Certainley that was not the case when I worked as an F/E for Qantas duringr a one year secondment on 747's in the mid 80's. The fire (or failure) would be announced and only on the handling pilot's command would the recall items be commenced.
It's as NoD says really in all airlines I've flown for.
Individual crew members should not take action that may affect the safe flight path of the aircraft unless that action has been agreed by the Captain, and furthermore any such action should be carefully monitored by another crew member.
Regards
Exeng