Evaporation of binary solutions confined in a 2D porous medium leads to the formation of labyrinthine patterns. We here demonstrate that the formation of these unusual out of equilibrium patterns occurs through a regular succession of bursts of individual meniscii. We identify the elementary mechanisms leading to the formation of crystal deposits at the pore scale and then establish a pore-network model that well captures the topology of the labyrinthine structures observed in our experiments as well as their dynamics. Using simple arguments, we predict topological changesin the drying pattern at the scale of an individual pore as the geometrical parameters of the problem and the contact angle are varied. Experiments confirm these predictions.