We present evidence that the time delay between the multiple rings of elves is not caused by the ground reflection of the electromagnetic pulse produced by intracloud lightning. To investigate temporal differences of multi-elves, we analyzed data from four storms occurring at various times and distances from the Pierre Auger Observatory in Malargüe, Argentina. The Auger fluorescence detector's high temporal resolution of 100 ns enabled the frequent observation of multi-elves, accounting for approximately 23% of the events. By examining the traces of 70 double and 24 triple elves, we demonstrate that the time delay between the rings remains relatively constant regardless of the arc distance to the lightning. These results deviate from the trend expected from the electromagnetic pulse (EMP) ground reflection model, which predicts a decreasing time delay with increasing arc distance from an intracloud lightning at a given height. The first emission ring is due to a direct path of the EMP to the ionosphere, with the reflected EMP creating the second ring. Simulations conducted with this model demonstrate that short energetic in-cloud pulses can generate four-peak elves, and a temporal resolution of at least 25 μ s is required to separate them. Therefore, temporal resolution is crucial in the study of multi-elves. Our observations in the Córdoba province, central Argentina, indicate that the current understanding of the mechanism generating these phenomena may be incomplete, and further studies are needed to assess whether multi-elves are more likely related to the waveform shape of the lightning than to its altitude.