When Tesla Inc. Chief Executive Elon Musk said the car maker would work around the clock to boost production of its Model 3 sedan, the number crunchers at Thasos Group decided to watch.

They circled Tesla’s 370 acres in Fremont, Calif., on an online map, creating a digital corral to isolate smartphone location signals that emanated from within it. Thasos, which leases databases of trillions of geographic coordinates collected by smartphone apps, set its computers to find the pings created at Tesla’s factory, then shared the...