Different circumstances demand different captaincy decisions. If it's just a fire warning light (!) it's probably less urgent that a big bang followed by a warning light.
As has already been stated, the most important priority is to fly the aircraft. Twenty five years ago I watched two pilots "kill" themselves due to incorrect diagnosis and actions following a fire warning in a twin engined helicopter. Thankfully this was only in the simulator!
I gave one a fire warning light (which was a spurious warning). The pilot, an overconfident ab initio, had just turned downwind. In his haste to carry out the full FRC Fire drills, without confirming anything, he lowered the lever far too much and then allowed the aircraft to fly him straight to the scene of the crash, still on the downwind leg. He was most most annoyed at me, his instructor, as he was convinced I'd failed both engines on him. I had done nothing except put on the fire warning light! I'd also taken the precaution of recording the whole thing (he was overconfident and tended to be "mouthy" in debriefs) and told him to sit back and watch the recording. He was astounded as the sim replicated his every move. Hopefully he learned his lesson; I'm sure he did because he went on to make Group Captain.
The second pilot was more worrying because he was more experienced. He was also prone to being far too rapid on the shutdown drills without correctly diagnosing the failure. Given a fire warning light on one engine, he closed down the wrong engine. Even worse, on a different sortie he shut down both when there was no need to do so. On that occasion he lowered the lever far too much for a single engine problem, watched the engines back off, and incorrectly assuming they had both failed, he went for the double engined emergency shutdown and failed to carry out a satisfactory EOL!
He was suitably debriefed and retrained. He later admitted that he had been criticised in his past for rushing emergency drills. Hopefully the sim training sorted him out once and for all.
