With the development of nuclear physics and detection technology, traditional analog data-acquisition (ADAQ) systems struggle to meet the demands of large-scale detection arrays. At the same time, digital data-acquisition (DDAQ) is widely employed due to the low per-channel cost, small dead time, and flexible parameter setting. However, high-precision time measurements remain a critical technical bottleneck for DDAQ, particularly when the desired resolution is smaller than the time interval between neighboring samples. Interpolated algorithms between adjacent samples must be used in order to get a better timing resolution. However, such Interpolated time information is significantly affected by the phase of signal, sampling rate, intrinsic pulse shape, discrimination parameters, and so on. The current work aims at quantifying the impacts of each aforementioned parameters on the timing precision in DDAQ. In this simulation work, the pulses are generated with different parameters, digitalized by an adjustable sampling rate, and then processed by a Digital Constant-Fraction discrimination (DCFD) algorithm. By modifying different parameters such as signal phase, pulse shape, and discrimination parameters, their impacts on timing precision have been investigated. The results conclusively confirm the strong influence of signal phase on the time accuracy in DDAQ. On the other side, if one wants the best time resolution, the rising time of nuclear pulses can neither be too short nor too long, namely, with 4–6 samples on the leading edge would be the best choice.