  We study $\mathcal{N}=2$ supersymmetric Jackiw-Teitelboim (JT) gravity at
finite temperature coupled to matter. The matter fields are related to
superconformal primaries by AdS/CFT duality. Due to broken super
reparametrisation invariance in the SCFT dual, there are corrections to
superconformal correlators. These are generated by the exchange of
super-Schwarzian modes which is dual to the exchange of 2D supergravity modes.
We compute corrections to four-point functions for superconformal primaries and
analyse the behaviour of out-of-time-ordered correlators. In particular,
four-point functions of two pairs of primaries with mutually vanishing
two-point functions are considered. By decomposing the corresponding
supermultiplet into its components, we find different Lyapunov exponents. The
value of the Lyapunov exponents depends on whether the correction is due to
graviton, gravitini or graviphoton exchange. If mutual two-point functions do
not vanish all components grow with maximal Lyapunov exponent.
