The network of observers are moving inertially (i.e. unpowered, freely falling), moving with the rocket for only a moment, so they're not accelerating like the rocket is. That's how those observers can make good measurements, in that moment. For more info search for "momentarily comoving inertial frame" at http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.ht.... Each inertial clock can measure the passage of time accurately.