  We report inelastic neutron scattering measurements of low energy ($\hbar
\omega < 10$ meV) magnetic excitations in the "11" system
Fe$_{1+y}$Te$_{1-x}$Se$_{x}$. The spin correlations are two-dimensional (2D) in
the superconducting samples at low temperature, but appear much more
three-dimensional when the temperature rises well above $T_c \sim 15$ K, with a
clear increase of the (dynamic) spin correlation length perpendicular to the Fe
planes. The spontaneous change of dynamic spin correlations from 2D to 3D on
warming is unexpected and cannot be naturally explained when only the spin
degree of freedom is considered. Our results suggest that the low temperature
physics in the "11" system, in particular the evolution of low energy spin
excitations towards %better satisfying the nesting condition for mediating
superconducting pairing, is driven by changes in orbital correlations.
