  The interplay between the nematic order and magnetism in FeSe is not yet well
understood. There is a controversy concerning the relationship between orbital
and spin degrees of freedom in FeSe and their relevance for superconductivity.
Here we investigate the effect of S substitution on the nematic transition
temperature ($T_{\rm n}$) and the low-energy spin fluctuations (SF) in FeSe
single crystals. We show that the low-energy SF emerge below the nematic
transition. The difference between the onset temperature for the critical SF
($T_{\rm SF}$) and $T_{\rm n}$ is small for FeSe but significantly increases
with S substitution. Below $T_{\rm SF}$ the Korringa relation is violated and
the effective muon hyperfine coupling constant changes a sign. Our results
exclude a direct coupling of the low-energy SF to the electronic nematic order
indicating a presence of multiple spin degrees of freedom in FeSe$_{\rm
1-x}$S$_{\rm x}$.
