Overcompensation means that the system jumps over the equilibrium point because the negative feedback is too strong. Then it returnes back and again jumps over the equilibrium. Continuous-time models with 1 variable never exhibit oscillations. In discrete-time models, oscillations are possible even with 1 variable. What causes oscillations is the delay between time steps.
Overcompensation is a result of large time steps.
If time steps were smaller, then the system would not jump over the equilibrium but will approach to it gradually. Now we will analyze stability in the Ricker's model. If a discrete time model has more than one state variable, then the analysis is similar to that in continuous-time models. The first step is to find equilibria. The second step is to linearize the model at the equilibrium state, i.e., to estimate the Jacobian matrix.