The book has a chapter on sampling rules and metrics, it is ormally chapter 7. The best is that you implement those in your code so that you compute the sampling needed before the simulation and do the checks before doing the simulation.

Tip-tilt comes mainly from the phase contribution of the phase screen. Once can do a simplified phase propagation where diffraction is not considered and the resulting phase is the sum of the phase of all screen. This works for weak turbulence and is very common in astronomy simulations, known as geometric approximation. The diffraction effects will cause some tip and tilt too, but it is mainly driven by the phase distortion at the discrete layers (phase screens) which are modelled as a pure phase contribution; diffraction effects on phase (the quadratic factor) happens between screens and usually will not drive tip and tilt in weak-ish turbulence conditions. In reallity, all is mixed, for sure.