Small is an adjective whose meaning is not absolutely defined, but only relatively to something.
In the case of the SMI the growing mode is the plasma wakefields mode.
This mode has (only) electric (in 1D) and magnetic (in 2 and 3D) fields and is supported by an electron plasma perturbation (density and currents).
Since in general the plasma is assumed to be homogeneous, uniform and fields and currents free, the quantity of reference for the SMI is the initial electron plasma density ne0.
The much heavier plasma ions are also in general assumed to be immobile at the typical time scale of the inverse of the electron plasma frequency.
Therefore, in the case of SMI, small means that the initial electron plasma density perturbation δne is small when compared to ne0.
Also, the initial electric fields (transverse and longitudinal) are small when compared to the cold plasma wave breaking field defined as Ewb=mecωpe/e.
Note that in the case of seeding of an instability (SMI or other) the initial mode amplitude may not be small.
Also, depending on the the parameters (beam and plasma), the saturated state of the SMI may correspond to wakefields in the linear or nonlinear wakefield regime, even though the evolution of the instability has evolved nonlinearly.
Note also that numerical simulations can (in principle) handle the linear and nonlinear regime of the instability and of the wakefields.