quantum mechanics - Do spin-spin interactions break time reversal symmetry?

I'm sure the answer is yes, but how is this shown? Normally for a single spin-1/2 you have a time reversal operator: $-i \sigma_y \hat{K}$ where $\sigma_y$ is the second Pauli matrix and $\hat{K}$ is the conjugation operator. How is this generalized to two spins?

I am thinking of whether or not interactions like exchange ($J \hat{S}_1 \cdot \hat{S}_2$) or the hyperfine interaction (contact Fermi: $a \hat{S} \cdot \hat{I}$) break time reversal symmetry.