Using a proprietary app called iSteer, Brian Tapp, a geologist for EOG Resources Inc., dashed off instructions to a drilling rig 100 miles away. This tool is among the reasons the little-known Texas company says it pumps more oil from the continental U.S. than Exxon Mobil Corp.—or any other producer. A rig worker received Mr. Tapp’s iPhone alert and tweaked the trajectory of a drill bit thousands of feet underground,…