Fort Irwin is a training base, and doesn't have access to satellite data feeds, global communications systems, or worldwide radiation monitoring (which is largely done by aircraft and satellites). It's quite possible that they could be unaware of the continued existence of Europe, the fleet at sea or overseas nuclear explosions.

There is a NASA satellite tracking center on the Fort Irwin Reservation, but I don't know if they can exercise any control over satellites, or tap their data feeds.

On the other hand, the Europeans should still have control of their satellites, and they might well have noticed two large nuke explosions in US territory. Their investigation could make for an interesting story.