The Shashlik tower is a significant component to measure the energy, time, and position of photons and electrons in the Electromagnetic Calorimeter (ECal), a vital detector of the Multi-Purpose Detector (MPD) in the Nuclotron-based lon Collider fAcility (NICA), Dubna, Russia. Based on the GEANT4 simulation toolkit, a variation of physical behavior in the tower was simulated, including the changes of photons during transmission, and used the rising edge detection method to measure the time-resolving ability of the module for natural muons and electron beams. Results show that 3 GeV electrons enter the tower, photons emitted by the scintillator are transmitted, 10665 photoelectrons are collected on Silicon Multipliers (SiPMs), yield is 3555 pe/GeV, and the light output is 0.16%. The time resolution of the module for muons is better than 160 ps, but the value of each tower is different. In addition, by changing the electron beam energy in the simulation, we observed that a larger number of photoelectrons collected by SiPMs leads to a better time resolution. At an electron beam energy of 1 GeV, the time resolution of the tower could be better than 101 ps. The simulated measuring results, and the methods of the tower photon transmission performance and the time resolution, will provide references and new optimum methods for subsequent experiential tests.