In multi-room environments, modelling the sound propagation is complex due to the coupling of rooms and diverse source-receiver positions. A common scenario is when the source and the receiver are in different rooms without a clear line of sight. For such source-receiver configurations, an initial increase in energy is observed, referred to as the "fade-in" of reverberation. Based on recent work of representing inhomogeneous and anisotropic reverberation with common decay times, this work proposes an extended parametric model that enables the modelling of the fade-in phenomenon. The method performs fitting on the envelopes, instead of energy decay functions, and allows negative amplitudes of decaying exponentials. We evaluate the method on simulated and measured multi-room environments, where we show that the proposed approach can now model the fade-ins that were unrealisable with the previous method.