The ability to control the properties of organic thin films is crucial for obtaining highly performant thin-film devices. However, thin films may experience post-growth processes, even when the most sophisticated and controlled growth techniques such as organic molecular beam epitaxy (OMBE) are used. Such processes can modify the film structure and morphology and, thus, the film properties ultimately affecting device performances. For this reason, probing the occurrence of post-growth evolution is essential. Equally importantly, the processes responsible for this evolution should be addressed in view of finding a strategy to control and, possibly, leverage them for driving film properties. Here, nickel-tetraphenylporphyrin (NiTPP) thin films grown by OMBE on highly oriented pyrolytic graphite (HOPG) are selected as an exemplary system exhibiting a remarkable post-growth morphology evolution consistent with Ostwald-like ripening. To quantitatively describe the growth, the height-height correlation function (HHCF) analysis of the atomic force microscopy (AFM) images is carried out, clarifying the role of the post-growth evolution as an integral part of the whole growth process. The set of scaling exponents obtained confirms that the growth is mainly driven by diffusion combined with the presence of step-edge barriers, in agreement with the observed ripening phenomenon. Finally, the results together with the overall approach adopted demonstrate the reliability of the HHCF analysis in systems displaying post-growth evolution.