Different pilots with different backgrounds would handle this situation differently. The specific terminology is discussed in some detail above. The courses of action taken depend a lot on the personalities of the characters you're trying to depict.

Those of us with experience in stranger parts of the industry can probably attest to the general levels of confusion and miscommunication that happen during the initial moments of a crisis.

So an experienced crew may spend a small but prudent amount of time establishing the facts so they can take the best course of action. The bomb or whatever isn't detonating immediately, so there'd be time to steer to an unpopulated area (probably not the allegheny national forest). There'd be time to coordinate with experts via phone-patch or direct satphone connection, get details of triggering, etc. There would also be a flood of extraneous communications occuring as airplanes get switched to discrete frequencies, ATC establishes fuel and souls on board, etc. So confusion rather order prevails in crisis. If you want to depict effective leadership, your crew will forge a semblance of order during this moment of devolving chaos.

With regard to some technical details, there are altitudes to optimize and minimize the effect of an air-burst, and consideration would be given to be at altitude high enough to avoid raising large amounts of debris into the atmosphere (which drastically affect the amount of radioactive fallout downwind).

It'd be believable and laudable to take an initial course to a place that you might think would be best to have some kind of event, but there'd be coorindation and a number of technical decisions occuring during this whole process.

There'd probably be a re-allocation of duties while the captain coordinated with company and experts. The first officer would probably take over control of the aircraft and ATC, etc.

Regarding jargon, there are a lot of ways these things can go down. You wouldn't be wrong ensuring everyone uses correct phraseology and even appropriate brevity. You wouldn't be wrong having things revert to plain-language or a mix thereof.

I'd focus on realism of the decisions and actions rather than the jargon. My two cents.