It is possible that the nanites had already been deployed, semi-dormant
, for several years, with the intent of eventually performing some kind of unified task. They had just enough internal power to replicate geometrically for a limited period of time and then stopped, waiting for a signal. The "Tower" was given the "order" and the single electronic communication bounced off all the comm satellites in orbit, waking up the nanites and activating them to their full energy-sucking potential. They may all have mini GPS transceivers, restricting certain groups to certain locales. That way, they could either be given individual group orders to attack certain nations, or a back door "scorched earth" order (that DOD boy obviously had programmed into the system) to wipe out everything on the planet.
It may not fully conform to the established plot (and what exactly happened at the tower does remain something of a mystery), but at least no magic is needed to rationalize the "global power outage in seconds" thing.