So...basically, John's employer and Jane's employer both simultaneously discover that the two are married, and then the two agencies *work together* to concoct an elaborate BatmanGambit wherein the two will kill each other. Why not just call their own agent in for a "regular meeting" in some secure location and then blow the place up while they are inside it? Or, if you really want to get both of them, arrange for both of them to be in the same building at the same time (indoors, not outdoors), and blow it up.
Look at it this way, two rival companies figure out that their best employees are working for each other. Neither one of them knows that they are rivals. Imagine that conversation between the employers "Hey, you kill your girl!" "I'm not killing my girl - you kill your guy!" "Well, he's my best agent." "She's my best agent!" "So what are we going to do? What's a fair way to settle this?" "Hey, he's your best. She's my best. Send them after each other. One takes the other out, or they take each other out. Is it on?" "It's on." The true fault lies in the fact that they didn't plan for the eventuality that they wouldn't kill each other.
An understandable mistake, they both probably assumed that their best assassins were sociopaths only using each other as a cover story and/or colluding with each other against the agency, not that they were actually in love.
Oh, while I'm at it — why did it take "5 or 6 years" for the employers to discover the marriage???
It might be that they knew about the marriage, but didn't know the true identity of the spouse. They probably don't know who all the agents of the rival agency are.
Indeed, note that John seems to be deliberately taking steps to foil detection of who he is even in his civilian life (the "faulty" answering machine that distorts his voice). Neither of them showed up on the radar as an agent to the rival company because they were both taking steps to make sure that didn't happen, they essentially just managed a double-blind coverup.
Why are two American agencies who apparently both normally target enemies of America be "rivals" to begin with? I can't see the CIA and NSA making their agents snuff each other over a marriage. Heck, I wouldn't be surprised if there ARE real life CIA and NSA agents who are married. The plot feels like cold war throwback that doesn't really hold up post cold war.
It's not overtly stated (or well implied), but the undertone is that neither John or Jane work for a government agency. That is, both agencies have a not-very-legal "private assassin-for-hire" feel to them. Or, at the very least, quasi-governmental agencies deep into illegal wetwork (assassinations on US soil being absolutely illegal for anyone to do).
So Jane's agency has a plan where, if the office is being invaded, they burn everything, shoot some grappling hooks to the building across the street, and escape. Fine. Very snazzy. But...John's one dude, with a handgun. There are six or seven other girls with Jane, presumably all of them also assassins. Pulling the scorched-earth contingency plan seems a little excessive. You've got him outnumbered, ladies, I think you can take'im.
That's not how her organization works. Jane's company clearly operates on protocol, procedure, and strict adherence to rules, as opposed to John's fast and loose mostly independent style. The procedure laid out when the base is compromised is to destroy everything and evacuate, so that's what they do. From a practical standpoint, there are many reasons for this: John has managed to sneak by their security so they don't know that it's only him, maybe he has a strike team with him. Maybe he told other people where he was going to be. Secrecy is clearly one of the company's most valuable assets, so they focus on making sure no one can track their actions rather than going all search & destroy on the intruder.
Jane herself consistently shows a character flaw. Namely, being great at elaborate contingency plans but lousy at improvising.