We examine the robustness of the color–color selection of quiescent galaxies (QGs) against contamination of dusty star-forming galaxies using the latest submillimeter data. We selected 18,304 QG candidates out to z ∼ 3 using the commonly adopted NUV–r–J selection based on the high-quality multiwavelength COSMOS2015 catalog. Using extremely deep 450 and 850 μm catalogs from the latest JCMT SCUBA-2 Large Programs, S2COSMOS and STUDIES, as well as the Atacama Large Millimeter/submillimeter Array submillimeter, VLA 3 GHz, and Spitzer MIPS 24 μm catalogs, we identified luminous, dusty, star-forming galaxies among the QG candidates. We also conducted stacking analyses in the SCUBA-2 450 and 850 μm images to look for less-luminous dusty galaxies among the QG candidates. By cross matching to the 24 μm and 3 GHz data, we were able to identify a subgroup of “IR-radio-bright” QGs that possess strong 450 and 850 μm stacking signals. The potential contamination of these luminous and less-luminous dusty galaxies accounts for approximately 10% of the color-selected QG candidates. In addition, there exists a spatial correlation between the luminous star-forming galaxies and the QGs at a ≲60 kpc scale. Finally, we found a high QG fraction among radio active galactic nuclei (AGNs) at z < 1.5. Our data show a strong correlation between QGs and radio AGNs, which may suggest a connection between the quenching process and the radio-mode AGN feedback.