The origin of the turbulent magnetic fields is not yet fully understood in galaxy clusters, especially in the outskirts and surroundings. The existence of these background magnetic fields influences the propagation of cosmic rays (CRs), especially with energy $E < 10^{18}$ eV. Understanding the topology and intensity of these diffuse fields can also help to elucidate the origin of the diffuse high-energy emission of neutrinos and gamma rays. Therefore, it is possible to investigate the origin of these emissions if we reproduce as accurately as possible the magnetic fields present in clusters of galaxies. The reverse is also true. We have developed a model to describe more realistically the magnetic field amplification and evolution in the intracluster medium (ICM) based on weakly collisional 3D MHD simulations of turbulent dynamo evolution with forced turbulence. We have included effective Braginskii viscosity and resistivity as well as small-scale kinetic instabilities which constrain the pressure anisotropy due to the low collisionality of this environment. The novelty of our model is the dynamic evolution of the viscosity coefficients, which is related to the back reaction of the increasing magnetic field on the plasma movements and the amplification and saturation of the dynamo process itself. We find that the magnetic fields amplify to values which are in agreement with those observed inside clusters. Also, the final viscosity decreases to values that align with the observations.