The adsorption of charged inverse micelles at the electrode-liquid interface has an important effect on field screening and on the voltage drop over diffuse double layers. Recently, we analyzed the behavior of inverse micelles in a nonpolar liquid close to this electrode-liquid interface. For the fluorocarbon/surfactant system under study, we are in the limit of slow adsorption and negligible desorption of inverse micelles on the electrodes. Upon applying a voltage step, this results in a measurable Stern layer buildup in the time range of hours clearly distinguishable from the diffuse double layer buildup, which happens in less than 1 s. This Stern layer buildup manifests itself by a shift in the voltage drop from the diffuse double layer to the Stern layer until the voltage drop over the Stern layers reaches the applied voltage, leaving a zero bulk field without the diffuse double layer. New measurements of the transients of Stern layer buildup show that the buildup of charges in the Stern layer is more complex. We explain the observed transient behavior by introducing an asymmetry in the adsorption rate of charged inverse micelles. We provide an equivalent electrical network, an analytical solution to explain the behavior in more detail, and simulations within the diffuse double layer limit for a range of adsorption rates.