We analyze the interplay between fluid inertia and thixotropy during the transient start-up dynamics of a fluidity model which captures the rheological behavior of aging soft (glassy) materials, in a rectilinear shear flow upon application of a step shear rate. We observe that when the steady-state flow curve is nonmonotonic, the system shows transient and/or apparent steady-state shear banding in close qualitative agreement with experimental observations. Due to competition between inhomogeneous aging and rejuvenation caused by fluid inertia during start up, we show that there is an apparent steady-state banding at large times (compared to the relevant momentum diffusion timescale) even for shear rates such that the steady state flow curve allows for a homogeneous flow. Thus, for aging soft glassy materials, the shear rate for achieving homogeneous flow is not necessarily given by the steady-state flow curve. We also observe that the transient and apparent steady-state shear banding behavior is not correlated to the negative slope of the stress-strain dependence during the transient. This work also emphasizes that in order to arrive at a realistic description of shear banding behavior in aging (thixotropic) soft materials, inertia may not always be neglected during the start-up dynamics. (C) 2018 The Society of Rheology.