We present 77Se-NMR measurements on FeSe1−xSx samples with sulfur content x=0%, 9%, 15%, and 29%. Twinned nematic domains are observed in the NMR spectrum for all samples except x=29%. The NMR spin-lattice relaxation rate shows that antiferromagnetic (AFM) fluctuations are initially enhanced between x=0% and x=9%, but are strongly suppressed for higher x values. The observed behavior of the AFM fluctuations parallels the superconducting transition temperature Tc in these materials, providing strong evidence for the primary importance of AFM fluctuations for superconductivity, despite the presence of nematic quantum criticality in the FeSe1−xSx system