Shape transformation and budding of phospholipid/fatty acid giant hybrid vesicles can be induced by an internal chemical stimulus (pH change) when coupled with an osmotic shock. In particular, an autocatalytic enzymatic reaction set (urea-urease system), confined in the lumen of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/oleic acid (HOA) vesicles, can force the budding of the hosting vesicle, when properly fed by a trans-membrane substrate infusion. Herein, we elucidate the budding mechanism by simulating the shape changes of a vesicle during the enzymatic reaction. The area-difference-elasticity (ADE) theory is thus implemented to minimize the surface elastic energy and obtain the equilibrium shape at different values of the reduced volume and different values of the reduced preferred area difference (Δa0). Simulations, together with control experiments, unambiguously show that to obtain an effective vesicle shape transformation, the osmotic stress and the pH change in the lumen of the vesicle must act in synergy at the same timescale. Osmotic pressure induces a vesicle deflation (volume loss), while the pH change affects the preferred area difference between the outer and the inner membrane leaflets.