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Core-collapse supernovae undergoing a first-order quantum chromodynamics (QCD) phase transition experience the collapse of the central protoneutron star that leads to a second bounce. This event is accompanied by the release of a second neutrino burst. Unlike the first stellar core bounce neutrino burst, which consists exclusively of electron neutrinos, the second burst is dominated by electron antineutrinos. Such a condition makes QCD supernovae an ideal site for the occurrence of fast neutrino flavor conversion (FFC), which can lead to rapid flavor equilibration and significantly impact the related neutrino signal. In this work, we perform a detailed analysis of the conditions for fast flavor instability around and after the second neutrino burst in QCD phase-transition supernova models launched from 25M circle dot and 40M circle dot progenitor models. We evaluate the relevant instability criteria and find two major phases of FFC. The first phase is closely associated with the collapse and the rapidly expanding shock wave, which is a direct consequence of the protoneutron star collapse due to the phase transition. The second phase takes place a few milliseconds later when electron degeneracy is restored near the protoneutron star surface. We also characterize the growth rate of fast flavor instability and estimate its impact on the evolution of the neutrino flavor content. The potential observational consequences on neutrino signals are evaluated by comparing a scenario assuming complete flavor equipartition with other scenarios without FFC. Finally, we investigate how FFC may influences r-process nucleosynthesis associated with QCD phase-transition-driven supernova explosions.