Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) are nowadays one of the most studied cell types, especially for their role as in vitro models to test drug safety. In the last decade, the amount of available in vitro data increased considerably, together with our understanding of hiPSC-CM electrophysiology. Experiments supported hiPSC-CM use as drug pre-screening models (e.g. in the CiPA initiative), but also partly dampened the initial enthusiasm because of hiPSC-CM structural immaturity. Here we propose an update of our recent Paci2018 hiPSC-CM model, focusing particularly on the mechanisms underlying the action potential (AP) automaticity. Indeed, one of the clearest markers of hiPSC-CM immaturity are the spontaneous APs. We reformulated the fast Na+ (INa) and the funny (If) currents to improve our previous fitting of in vitro experiments and we kept the Paci2018 formulations of K+ currents (IKr, IKs, IK1 and Ito) and late Na+ (INaL) and L-type Ca2+ (ICaL) currents. We then used an optimization framework to automatically identify the parameters formalizing currents/mechanisms for which in vitro data were not available. We identified a model producing APs and Ca2+ transients in agreement with literature and our in-house data. Especially, we showed how also the Na+/Ca2+ exchanger (INCX) has an important role sustaining the AP automaticity: in fact, a strong (90%) INCX block suppresses the spontaneous APs, in agreement with in vitro data. The new Paci2019 was further validated against the in vitro experiments used for the Paci2018 model, showing that this update did not affect the capability of the new model to simulate mechanisms (e.g. responses to drugs or proarrhythmic events) successfully reproduced by the previous model. In conclusion, the Paci2019 model represents an improved tools for in silico studies on e.g. hiPSC-CM drug responses still keeping all the good features of its previous version.