First of all, these training exercises have the highest concentration of military-grade sensors in the world. In the history of the world. And I don’t mean that in the cliche way that military-grade sensors are good per se. Just that civilian sensors designed to detect hiding aircraft don’t really exist.
And you only get these concentrations in training exercises because the world’s most cutting edge military hasn’t had a war against a technologically advanced opponent in decades. Decades during which those sensors have become increasingly sensitive and networked with a greater quantity of supplementary data sources and somewhat complex algorithms for blending data from many sensors. All of which means of course it’s a military detection, and of course it’s a training exercise (DOD would also almost certainly not release operational information, even in summary, so we can safely assume any detections in an operational environment remain classified).