The proton-proton momentum correlation functions [C-pp(q)] for the kinematically complete decay channels Al-23 -> p + p + Na-21 and Mg-22 -> p + p + Ne-20 have been measured at the RIKEN RI Beam Factory. From the very different correlation strength of C-pp(q) for Al-23 and Mg-22, the source size and emission time information were extracted from the C-pp(q) data by assuming a Gaussian source profile in the correlation function calculation code (CRAB). The results indicated that the mechanism of two-proton emission from Al-23 was mainly sequential emission, while that of Mg-22 was mainly three-body simultaneous emission. By combining our earlier results of the two-proton relative momentum and the opening angle, it is pointed out that the mechanism of two-proton emission could be distinguished clearly.