The photodynamics of the Green Fluorescent Protein (GFP) has been addressed in detail, particularly by means of Fluorescence Correlation Spectroscopy (FCS), a technique that provides direct information when the diffusion and the photodynamics time scales are well separated. Efficient photoswitchable GFPs, a crucial component for applications in nanoscopy imaging, have long residence times in the dark state, typically longer than the diffusion time of the protein through the observation volume. In these cases, the effect of the coupling between photodynamics and the diffusion process on the analysis of the FCS measurements cannot be disregarded, and the use of FCS methods becomes therefore critical. This work deals with the analytical and simulative study of such coupling and indicates that the corrections to be applied to the conventional decoupled FCS model scale as the square root of the ratio between the diffusion and the dark state relaxation times. We discuss the possibility to estimate the extent of the diffusion/photodynamics coupling from the analysis of the inverse of the fluorescence autocorrelation function g(t), defined as G(-1)(g(t)) = g(0)/g(t) - 1. The function G(-1)(g(t)) is analyzed in terms of a parabolic expansion in which the curvature term directly provides the desired measure of the coupling. We validate the analytical prediction and the graphical estimate of the coupling on simulations of FCS experiments that are based on a coupled Monte Carlo-Brownian Dynamics algorithm. The analysis of the curvature of (g(0), applied to experimental FCS data of the photoswitchable E222Q mutant of GFPMut2 (Mut2Q), indicates that the trapping rate for this chromophore is 3 orders of magnitude underestimated when the diffusion/photodynamics coupling is not taken into account and sheds some additional light on the complex energy diagram for this protein.