What you noted is sufficient for anisotropic plasticity (Hill potential) with kinematic hardening.
I was a little confused by your description, though. If you want to have combined hardening (isotropic + kinematic), you need to use Chaboche model - details are in the documentation. Regular kinematic hardening model is not combined with isotropic hardening since they are different/mutually exclusive; however, Chaboche is a nonlinear kinematic hardening model that can account for addition with isotropic hardening.
The solver takes care of the back stress and change in yield stress calculations for each integration point.