Shear step strain experiments with various strain amplitudes have been performed on poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate) (PMMA) melts using both stress-controlled and strain-controlled rheometers. Firstly, the onset of the rheological nonlinearity, i.e., nonlinear stress damping behavior, occurring after a large step strain is found to be a phenomenological consequence of an abrupt stress decline within the transient period of strain actuation. Such a feature, analogous to the stress overshoot in a fast startup shear with sufficiently high rates, is interpreted based on theoretical frameworks concerning chain disentanglement/re-entanglement arising from chain retraction. Furthermore, this work infers that full technical considerations in step strain experiments are indispensable for acquisition of accurate stress relaxation data, as some common but easily overlooked technical problems are influential, probably introducing errors. For instance, a too long finite rise time and a stress overload enable to hinder the nonlinearity onset in the transient period, resulting in inaccurate experimental data. In this sense, the stress-controlled rheometer is advantageous relative to the strain-controlled one, although the inertia in the stress-controlled mode incurs a strain overshoot effect. Nevertheless, the amplitude-dependent strain overshoot offers a very subtle effect on the stress damping behavior. Moreover, transducer compliance problems need to be taken into account, especially for high stiffness polymers. Overall, the effects of such technical factors are dictated by their ability to influence the chain stretching/retraction and the disentanglement. A well-considered experimental methodology is necessary to achieve confidence windows in step strain experiments for analysis accuracy.