I can see the point of short code phrases being useful to communicate to all staff that they need to instigate certain actions but unless they have an innocuous meaning to passengers they are bound to cause panic to passengers with a resultant risk of panic, stress and associated unpredictable behaviour.
A well handled emergency such as this one involves many phases. There is often a "critical " phase where the problem first manifests itself. Once that phase has been resolved, it doesn't mean the emergency has ended. For example an engine fire that results in an engine shutdown still results in the aircraft operting in a performance limited envelope with all (in the case of a twin engined airliner) of the redundancy capability utilized. That would necessitate a diversion to the departure airport, or another nearby airport. It can also happen that secondary effects of the primary emergency are not immediately apparant.
It is conceivable that in some situations it may be necessary to evacuate everybody on board shortly after landing. As such, a bit of "panic and stress" is no bad thing, in that it should raise adrenelin levels. Perhaps they will be raised to the level that a few people who thought it was unnecessary to read the safety card, will now have less qualms about reading it. In any event the cabin crew will carry out the requisite procedures in accordance with their own training and in accordance with the situation as it manifests itself.
Surely the senior cabin crew would already be on their way to the flight deck having heard the loud bangs and been alerted by the passengers reaction to the sheets of flame!
No, they react to the communication that has already been given as is appropriate to the situation.
I think any ordinary passenger would find the use of blatant code words rather disconcerting and would be worried about what they are hiding.
They might, but as already pointed out, they are not "hiding" anything, and in the example you have given I would imagine the "loud bangs & sheets of flame" might worry them a little bit as well. I am sure they would cause more than a little consternation to the crew come to that. The procedures for resolving these rare situations are what everybody is trained for, and it is of primary importance that this training is utilized with communication procedures that have been established for the purpose, without any other non essential concerns at that point.