Synchronized time-lens source is a novel method to generate synchronized optical pulses to mode-locked lasers, and has found widespread applications in coherent Raman scattering microscopy. Relative timing jitter between the mode-locked laser and the synchronized time-lens source is a key parameter for evaluating the synchronization performance of such synchronized laser systems. However, the origins of the relative timing jitter in such systems are not fully determined, which in turn prevents the experimental efforts to optimize the synchronization performance. Here, we demonstrate, through theoretical modeling and numerical simulation, that the photodetection could be one physical origin of the relative timing jitter. Comparison with relative timing jitter due to the intrinsic timing jitter of the mode-locked laser is also demonstrated, revealing different qualitative and quantitative behaviors. Based on the nature of this photodetection-induced timing jitter, we further propose several strategies to reduce the relative timing jitter. Our theoretical results will provide guidelines for optimizing synchronization performance in experiments.