There is a long standing debate about whether or not the annual modulation signal reported by the DAMA/LIBRA collaboration is induced by Weakly Interacting Massive Particles~(WIMP) in the galaxy's dark matter halo scattering from nuclides in their NaI(Tl) crystal target/detector. This is because regions of WIMP-mass vs. WIMP-nucleon cross-section parameter space that can accommodate the DAMA/LIBRA-phase1 modulation signal in the context of the standard WIMP dark matter galactic halo and isospin-conserving~(canonical), spin-independent~(SI) WIMP-nucleon interactions have been excluded by many of other dark matter search experiments including COSINE-100, which uses the same NaI(Tl) target/detector material. Moreover, the recently released DAMA/LIBRA-phase2 results are inconsistent with an interpretation as WIMP-nuclide scattering via the canonical SI interaction and prefer, instead, isospin-violating or spin-dependent interactions. Dark matter interpretations of the DAMA/LIBRA signal are sensitive to the NaI(Tl) scintillation efficiency for nuclear recoils, which is characterized by so-called quenching factors~(QF), and the QF values used in previous studies differ significantly from recently reported measurements, which may have led to incorrect interpretations of the DAMA/LIBRA signal. In this article, the compatibility of the DAMA/LIBRA and COSINE-100 results, in light of the new QF measurements is examined for different possible types of WIMP-nucleon interactions. The resulting allowed parameter space regions associated with the DAMA/LIBRA signal are explicitly compared with 90\% confidence level upper limits from the initial 59.5~day COSINE-100 exposure. With the newly measured QF values, the allowed 3\(\sigma\) regions from the DAMA/LIBRA data are still generally excluded by the COSINE-100 data.