The Wilson-Cowan model is a well-known population model that represents the collective dynamics of two subpopulations: excitatory and inhibitory. It is the subject of many phase transition papers that study neuronal networks at a men-field level. The stochastic version was written in the past decade and brought with it the study of noisy dynamics, e.g., avalanches, in the aforementioned phases. The model shows the possibility of a stable quiescent phase, which piqued our interest in quiescent to active phase transitions. Our work scrutinizes the plethora of transitions with different behaviors (i.e., discontinuous or continuous) shown in this model. In particular, we show transitions that belong to known universality classes, mean-field directed percolation (MF-DP) and mean-field tricritical directed percolation (MF-TDP); and novel universality classes. The novel behavior of the system includes a new continuous transition that shows new exponents and breaks scaling relations, as well as three seemingly continuous transitions without the common hallmarks of a bonafide second-order phase transition. Our goal is to broaden the current knowledge of criticality when one introduces inhibitory units.