Laser-accelerated ion sources have exceptional properties and could stimulate development of compact ion accelerators. For many applications beam control is an essential requirement. A new and interesting technique to control proton beam characteristics has been recently developed. It consists in using an ultrafast laser-triggered micro-lens, which provides simultaneous energy selection and focusing of the incoming ion beam and is tunable. Particle-in-cell simulations coupled with particle tracing are used to model the focusing and energy selection mechanisms, and to study the symmetry of the expanding plasma inside the micro-lens. The model developed is able to reproduce and explain the experimental results obtained at the Laboratoire pour l'Utilisation des Lasers Intenses in France.