The only authorative version of events is in the Indian AAIB interim report and it does not say quite that with respect to actions and timings
All it says is basically the two fuel control switches went to cut off just after lift off...about ten seconds later they went back on, and at some point within those ten seconds there was a brief discussion.....so we don't know how long it took for the fuel control switch positions to be noticed.
I'd kind of speculate that for the first handful of those seconds there will have been a ???..first symptoms on the flight deck might have been generator warnings plus a sensation of loss of thrust, flight path decaying, engine parameters beginning to wind down, maybe plus audio alerts.
I'd speculate, again, that the obvious place for the pilots to check initially would be systems like fuel pump switches and other switches on the overhead panel...I'm not sure anyone analysing this rationally would be looking downwards at first at the fuel cutoff switches because there would be no rational reason to think they would have been moved..
...then there's the,.to.paraphrase "who did that", then they get moved back to run...
All takes time...
Worth bearing in mind it took Sullenberger about ten seconds to call for any major actions in the Hudson accident, and he knew he'd hit birds.