Stirling-type pulse tube cryocoolers (SPTCs) working at liquid-helium temperatures are appealing in space applications because of their promising advantages such as high reliability, compactness, etc. Worldwide efforts have been put in to develop SPTCs operating at liquid-helium temperatures especially with helium-4 as the working fluid. Staged structure is essential to reach such low temperatures. Generally, both the regenerator of the last section and the pulse tube together with the phase shifter are precooled by its upper stage or by external cold source to a low temperature of around 20 K. However, the precooling effects on the regenerator and the pulse tube are synthetic in previous studies, and their independent effects have not been studied clearly. In this manuscript, the precooling effects on the regenerator and on the pulse tube together with the phase shifter are tested independently on a unique-designed precooled SPTC. The tested precooling temperature is between 13.3 K and 22 K, and the no-load refrigeration temperature gets down to 3.6 K. Further analyses and numerical calculations have been carried out. It is found that the influence on the regenerator is remarkable, which is different from previous conclusions. It is also found that the precooling effects on the pulse tube are relatively weak because of the large pressure-induced enthalpy flow of a real gas working at the temperatures near to the critical point. Furthermore, the phase shifting capacity is analyzed with two cases and with both helium-4 and helium-3 as working fluids, and it keeps quite constant after optimizing the frequency and the precooling temperature for each case. The investigation on these independent effects will provide valid reference on the precooling mechanism study of SPTCs working down to liquid-helium temperatures.