The short-time scaling behaviour of the critical dynamics for the two-dimensional Ising model and Potts model are investigated with both the heat-bath and the Metropolis algorithm. Special attention is drawn to universality. We observed that the microscopic time scale tmic after which the universal scaling behaviour appears is not always negligibly small. Taking carefully the effect of tmic into account, the critical exponents are extracted from the power law behaviour of the observables in the beginning of the time evolution. All the results are consistent and therefore universality and scaling are confirmed.